# on 18-Apr-2017 (Tue)

#### Flashcard 1432470031628

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#nature-of-language #sister-miriam-joseph #trivium
Question
A word is a [...].
symbol

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A word is a symbol. Its matter is the sensible sign; its form is the meaning imposed upon it by convention.

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#### Flashcard 1432867704076

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#i-q #types-of-inteligence
Question
[...], e.g. numerical aptitude, problem solving, deciphering codes, abstract symbols and formulae.
Logic=mathematic

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Logic=mathematic, e.g. numerical aptitude, problem solving, deciphering codes, abstract symbols and formulae.

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#### Flashcard 1439710448908

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Question
To estimate the cost of capital of a contemplated project you [...] and adjust it to reflect the risk of the contemplated project.
estimate the company's cost

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mpany must estimate project-specific costs of capital. What is often done, however, is to estimate the cost of capital for the company as a whole and then adjust this overall corporate cost of capital upward or downward to reflect the risk of <span>the contemplated project relative to the company’s average project.<span><body><html>

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1. INTRODUCTION
ital is a central issue in corporate financial management. For the analyst seeking to evaluate a company’s investment program and its competitive position, an accurate estimate of a company’s cost of capital is important as well. <span>Cost of capital estimation is a challenging task. As we have already implied, the cost of capital is not observable but, rather, must be estimated. Arriving at a cost of capital estimate requires a host of assumptions and estimates. Another challenge is that the cost of capital that is appropriately applied to a specific investment depends on the characteristics of that investment: The riskier the investment’s cash flows, the greater its cost of capital. In reality, a company must estimate project-specific costs of capital. What is often done, however, is to estimate the cost of capital for the company as a whole and then adjust this overall corporate cost of capital upward or downward to reflect the risk of the contemplated project relative to the company’s average project. This reading is organized as follows: In the next section, we introduce the cost of capital and its basic computation. Section 3 presents a selection of methods for estimat

#### Flashcard 1440228969740

Tags
#cfa-level-1 #factors-that-determine-market-structures #microeconomics #reading-16-the-firm-and-market-structures #section-2-analysis-of-mkt-structures #study-session-4
Question
When the market dictates the price based on [...] , the individual firm has no control over pricing
aggregate supply and demand conditions

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When the market dictates the price based on aggregate supply and demand conditions, the individual firm has no control over pricing. The typical hog farmer in Nebraska and the milk producer in Bavaria are price takers . That is, they must accept whatever price the market dictates. This is the case under the market s

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2. ANALYSIS OF MARKET STRUCTURES

#### Flashcard 1442135018764

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Question
Analysts' interest in valuation coincides with the capital budgeting focus of [...]
maximizing shareholder value.

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although analysts have a vantage point outside the company, their interest in valuation coincides with the capital budgeting focus of maximizing shareholder value.

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1. INTRODUCTION
security analysts and portfolio managers are based on capital budgeting methods. Conversely, there have been innovations in security analysis and portfolio management that have also been adapted to capital budgeting. Finally, <span>although analysts have a vantage point outside the company, their interest in valuation coincides with the capital budgeting focus of maximizing shareholder value. Because capital budgeting information is not ordinarily available outside the company, the analyst may attempt to estimate the process, within reason, at least for companies that are not too complex. Further, analysts may be able to appraise the quality of the company’s capital budgeting process—for example, on the basis of whether the company has an accounting focus or an economic focus. This reading is organized as follows: Section 2 presents the steps in a typical capital budgeting process. After introducing the basic principles of capital budgeti

#### Flashcard 1442536099084

Tags
#cfa #cfa-level-1 #economics #lol #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-2-objectives-of-the-firm #study-session-4
Question
Objectives can be classified in profitability or on [...]
controlling risk

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When managers of for-profit companies have been surveyed about the objectives of the companies they direct, researchers have often concluded that a) companies frequently have multiple objectives; b) objectives can often be classified as focused on profitability (e.g., maximizing profits, increasing market share) or on controlling risk (e.g., survival, stable earnings

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2. OBJECTIVES OF THE FIRM
be known with certainty (i.e., the theory of the firm under conditions of certainty). The main contrast of this type of analysis is to the theory of the firm under conditions of uncertainty, where prices, and therefore profit, are uncertain. <span>Under market uncertainty, a range of possible profit outcomes is associated with the firm’s decision to produce a given quantity of goods or services over a specific time period. Such complex theory typically makes simplifying assumptions. When managers of for-profit companies have been surveyed about the objectives of the companies they direct, researchers have often concluded that a) companies frequently have multiple objectives; b) objectives can often be classified as focused on profitability (e.g., maximizing profits, increasing market share) or on controlling risk (e.g., survival, stable earnings growth); and c) managers in different countries may have different emphases. Finance experts frequently reconcile profitability and risk objectives by stating that the objective of the firm is, or should be, shareholder wealth maximization (i.e.,

#### Flashcard 1442615004428

Tags
#estructura-interna-de-las-palabras #formantes-morfológicos #gramatica-española #la #morfología #tulio
Question
Cual es la estructura interna de la palabra gota?
Carece de estructura interna.

Es una palabra simple.

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fológico o morfema es una unidad mínima que consta de una forma fonética y de un significado. Comparemos las siguientes palabras: gota, gotas, gotita, gotera, cuentagotas. Gota es la única de estas palabras que consta de un solo formante. <span>Carece, entonces, de estructura interna. Es una palabra simple. Todas las otras palabras tienen estructura interna. [31] Los formantes que pueden aparecer como palabras independientes son formas libres. Los otros, los que necesariamente van adosados a otros morfe- mas, son formas ligadas

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La estructura interna de la palabra

#### Flashcard 1443061697804

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Question
An investor in [...] is concerned about the company’s ability to pay dividends and the likelihood that its share price will increase.
equity securities

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An investor in equity securities is an owner with a residual interest in the company and is concerned about the company’s ability to pay dividends and the likelihood that its share price will increase.</b

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1. INTRODUCTION
viding capital to companies—specifically, whether to invest in the company’s debt or equity securities and at what price. An investor in debt securities is concerned about the company’s ability to pay interest and to repay the principal lent. <span>An investor in equity securities is an owner with a residual interest in the company and is concerned about the company’s ability to pay dividends and the likelihood that its share price will increase. Overall, a central focus of financial analysis is evaluating the company’s ability to earn a return on its capital that is at least equal to the cost of that capital, to profitably grow

#### Flashcard 1443108097292

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Question

Cash flow is important because, ultimately, the company needs cash to [...] in order to continue as a going concern.

pay employees, suppliers, and others

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wes for the goods it had purchased on credit in the prior month. Although profitability is important, so is a company’s ability to generate positive cash flow. Cash flow is important because, ultimately, the company needs cash to <span>pay employees, suppliers, and others in order to continue as a going concern. A company that generates positive cash flow from operations has more flexibility in funding needed for investments and taking advantage of attra

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2. SCOPE OF FINANCIAL STATEMENT ANALYSIS
d to earn that income. Overall, profit (or loss) equals income minus expenses, and its recognition is mostly independent from when cash is received or paid. Example 1 illustrates the distinction between profit and cash flow. <span>EXAMPLE 1 Profit versus Cash Flow Sennett Designs (SD) sells furniture on a retail basis. SD began operations during December 2009 and sold furniture for €250,000 in cash. The furniture sold by SD was purchased on credit for €150,000 and delivered by the supplier during December. The credit terms granted by the supplier required SD to pay the €150,000 in January for the furniture it received during December. In addition to the purchase and sale of furniture, in December, SD paid €20,000 in cash for rent and salaries. How much is SD’s profit for December 2009 if no other transactions occurred? How much is SD’s cash flow for December 2009? If SD purchases and sells exactly the same amount in January 2010 as it did in December and under the same terms (receiving cash for the sales and making purchases on credit that will be due in February), how much will the company’s profit and cash flow be for the month of January? Solution to 1: SD’s profit for December 2009 is the excess of the sales price (€250,000) over the cost of the goods that were sold (€150,000) and rent and salaries (€20,000), or €80,000. Solution to 2: The December 2009 cash flow is €230,000, the amount of cash received from the customer (€250,000) less the cash paid for rent and salaries (€20,000). Solution to 3: SD’s profit for January 2010 will be identical to its profit in December: €80,000, calculated as the sales price (€250,000) minus the cost of the goods that were sold (€150,000) and minus rent and salaries (€20,000). SD’s cash flow in January 2010 will also equal €80,000, calculated as the amount of cash received from the customer (€250,000) minus the cash paid for rent and salaries (€20,000) and minus the €150,000 that SD owes for the goods it had purchased on credit in the prior month. Although profitability is important, so is a company’s ability to generate positive cash flow. Cash flow is important because, ultimately, the company needs cash to pay employees, suppliers, and others in order to continue as a going concern. A company that generates positive cash flow from operations has more flexibility in funding needed for investments and taking advantage of attractive business opportunities than an otherwise comparable company without positive operating cash flow. Additionally, a company needs cash to pay returns (interest and dividends) to providers of debt and equity capital. Therefore, the expected magnitude of future cash flows is important in valuing corporate securities and in determining the company’s ability to meet its obligations. The ability to meet short-term obligations is generally referred to as liquidity , and the ability to meet long-term obligations is generally referred to as solvency . Cash flow in any given period is not, however, a complete measure of performance for that period because, as shown in Example 1, a company may be obligated to make future cash payments as a result of a transaction that generates positive cash flow in the current period. Profits may provide useful information about cash flows, past and future. If the transaction of Example 1 were repeated month after month, the long-term average monthly cas

#### Flashcard 1444545432844

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Question
The role of financial statement analysis is to use financial reports prepared by companies, combined with other information, to evaluate the [...], [...] , and [...] and financial position of a company for the purpose of making investment, credit, and other economic decisions.
past

current

potential performance

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The role of financial statement analysis is to use financial reports prepared by companies, combined with other information, to evaluate the past, current, and potential performance and financial position of a company for the purpose of making investment, credit, and other economic decisions.

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2. SCOPE OF FINANCIAL STATEMENT ANALYSIS
The role of financial reporting by companies is to provide information about a company’s performance, financial position, and changes in financial position that is useful to a wide range of users in making economic decisions.1 The role of financial statement analysis is to use financial reports prepared by companies, combined with other information, to evaluate the past, current, and potential performance and financial position of a company for the purpose of making investment, credit, and other economic decisions. (Managers within a company perform financial analysis to make operating, investing, and financing decisions but do not necessarily rely on analysis of related financial statements. They have access to additional financial information that can be reported in whatever format is most useful to their decision.) In evaluating financial reports, analysts typically have a specific economic decision in mind. Examples of these decisions include the following: Evalu

#### Flashcard 1446743248140

Tags
#cfa-level-1 #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4
Question

The quantity sold can be affected by the business through such activities as sales promotion, advertising, and competitive positioning of the product that would take place under the market model of [...].

imperfect competition

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willing and able to buy at each price level. The quantity sold can be affected by the business through such activities as sales promotion, advertising, and competitive positioning of the product that would take place under the market model of <span>imperfect competition. Under perfect competition, however, total quantity in the market is influenced strictly by price, while non-price factors are not important. Once consumer preferences are established i

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3. ANALYSIS OF REVENUE, COSTS, AND PROFITS
(AR) Marginal Revenue (MR) 0 100 0 — — 1 100 100 100 100 2 100 200 100 100 3 100 300 100 100 4 100 400 100 100 5 100 500 100 100 6 100 600 100 100 7 100 700 100 100 8 100 800 100 100 9 100 900 100 100 10 100 1,000 100 100 <span>The quantity or quantity demanded variable is the amount of the product that consumers are willing and able to buy at each price level. The quantity sold can be affected by the business through such activities as sales promotion, advertising, and competitive positioning of the product that would take place under the market model of imperfect competition. Under perfect competition, however, total quantity in the market is influenced strictly by price, while non-price factors are not important. Once consumer preferences are established in the market, price determines the quantity demanded by buyers. Together, price and quantity constitute the firm’s demand curve, which becomes the basis for calculating the total, average, and marginal revenue. In Exhibit 4, price is the market price as established by the interactions of the market demand and supply factors. Since the firm is a price taker, price is fixed at 100

#### Flashcard 1446843387148

Tags
#estructura-interna-de-las-palabras #formantes-morfológicos #gramatica-española #la #morfología #tulio
Question
Las palabras que contienen un afijo se denominan [...]
palabras complejas.

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pan>Algunos afijos van pospuestos a la base (gota), como los de nuestros ejemplos: son los s u f i j o s . Otros afijos la preceden: in-útil, des-contento, a-político: Son los prefijos. Las palabras que contienen un afijo se denominan palabras complejas.<span><body><html>

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La estructura interna de la palabra

#### Flashcard 1446897913100

Tags
#cfa-level-1 #economics #has-images #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4

Question
The production function has three distinct regions where both the direction of change and the rate of change in total product (TP or Q, quantity of output) vary as production changes. Regions 1 and 2 have [...] in TP as labor is added, but the change turns [...] in Region 3.
positive changes

Negative changes

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The production function has three distinct regions where both the direction of change and the rate of change in total product (TP or Q, quantity of output) vary as production changes. Regions 1 and 2 have positive changes in TP as labor is added, but the change turns negative in Region 3.

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This image illustrates the shape of a typical input–output relationship using labor (L) as the only variable input (all other input factors are held constant). The production function has three distinct regions where both the direction of change and the rate of change in total product (TP or Q, quantity of output) vary as production changes. Regions 1 and 2 have positive changes in TP as labor is added, but the change turns negative in Region 3. Moreover, in Region 1 (L 0 – L 1 ), TP is increasing at an increasing rate, ty

#### Flashcard 1447231098124

Tags
#sister-miriam-joseph #trivium
Question
Language that symbolizes an individual or aggregate

[...]

[...]
proper name

particular or empirical description

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Language that symbolizes an individual or aggregate proper name particular or empirical description

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#### Flashcard 1447238438156

Tags
#sister-miriam-joseph #trivium
Question
A common name or a general description must represent an [...] or [...] which is intrinsically possible although it need not actually exist.
essence

class nature

Otherwise, it is devoid of meaning as are a square circle or a triangular square.

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A common name or a general description must represent an essence or class nature which is intrinsically possible although it need not actually exist. Otherwise, it is devoid of meaning as are a square circle or a triangular square.</bod

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#### Flashcard 1447288769804

Tags
#sister-miriam-joseph #trivium
Question
The things in a room constitute an [...] belonging to [...] ,
aggregate of individuals

different species

such as chair, desk, table, book, heat vent, window, etc., but they are only a small part of each species.

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The things in a room constitute an aggregate of individuals belonging to different species, such as chair, desk, table, book, heat vent, window, etc., but they are only a small part of each species.

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#### Flashcard 1447506087180

Tags
#7-important-definitions #language-and-reality #sister-miriam-joseph #trivium
Question
Even if individuals were as alike as the matches in a box of matches, they would be individually different because [...] but is a different quantity or part even though of the same kind and amount.
the matter in one is not the matter in the other

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Even if individuals were as alike as the matches in a box of matches, they would be individually different because the matter in one is not the matter in the other but is a different quantity or part even though of t he same kind and amount.

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#### Flashcard 1448189758732

Tags
#sister-miriam-joseph #trivium
Question
An allusion depends for much of its effect on the [...] dimension of language.
psychological

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An allusion depends for much of its effect on the psychological dimension of language, for it enriches the passage in which it occurs with emotional overtones and associated ideas derived from the context in which it originally appeared.</spa

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#### Flashcard 1448327122188

Tags
#cfa-level-1 #economics #has-images #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4

Question

Total revenue increases with a greater quantity, but [...] as quantity increases.

Average revenue and marginal revenue decrease when output increases, with MR falling faster than price and AR.

Average revenue is equal to price at each quantity level.

This shows the relationships among the revenue variables.

the rate of increase in TR (as measured by marginal revenue) declines

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Total revenue increases with a greater quantity, but the rate of increase in TR (as measured by marginal revenue) declines as quantity increases. Average revenue and marginal revenue decrease when output increases, with MR falling faster than price and AR. Average revenue is equal to p

#### Flashcard 1448430931212

Tags
#sister-miriam-joseph #symbols-from-reality #trivium
Question

First the [...] operate on an object present before us and produce a percept.

Then the [...] , primarily the imagination, produce a phantasm or mental image of the individual object perceived,
external senses

internal senses

This phantasm is retained and can be reproduced at will in the absence of the object.

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First the external senses operate on an object present before us and produce a percept. The internal senses, primarily the imagination, produce a phantasm or mental image of the individual object

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#### Flashcard 1448524516620

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Question
An analyst may value shares of a company by comparing its price-to-earnings ratio (P/E) to the P/Es of [...] .
peer companies

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Earnings are also frequently used by analysts in valuation. For example, an analyst may value shares of a company by comparing its price-to-earnings ratio (P/E) to the P/Es of peer companies and/or may use forecasted future earnings as direct or indirect inputs into discounted cash flow models of valuation.

#### Flashcard 1448530283788

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Question
The [...] can be measured by comparing the resources controlled by the company in relation to the claims against those resources.
financial position

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The financial position can be measured by comparing the resources controlled by the company ( assets ) in relation to the claims against those resources ( liabilities and equity ).

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Analysts are also interested in the current financial position of a company. The financial position can be measured by comparing the resources controlled by the company ( assets ) in relation to the claims against those resources ( liabilities and equity ). An example of a resource is cash. In Example 1, if no other transactions occur, the company should have €230,000 more in cash at 31 December 2009 than at the start of the period. The ca

#### Flashcard 1448537361676

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Question
The role of financial reporting is to provide information about a company's financial position and performance for use by parties both [...] and [...] to the company.
internal

externa

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The role of financial reporting is to provide information about a company's financial position and performance for use by parties both internal and external to the company.

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Subject 1. The Roles of Financial Reporting and Financial Statement Analysis
The role of financial reporting is to provide information about a company's financial position and performance for use by parties both internal and external to the company. Financial statements are issued by management, who is responsible for their form and content. The role of financial statement analysis, on the other hand, is to take these

#### Flashcard 1448544963852

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Question
The role of [...], on the other hand, is to take these financial statements and other information to evaluate the company's past, current, and prospective financial position and performance for the purpose of making rational investment, credit, and similar decisions.

financial statement analysis

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The role of financial statement analysis, on the other hand, is to take these financial statements and other information to evaluate the company's past, current, and prospective financial position and performance for the purpo

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Subject 1. The Roles of Financial Reporting and Financial Statement Analysis
provide information about a company's financial position and performance for use by parties both internal and external to the company. Financial statements are issued by management, who is responsible for their form and content. <span>The role of financial statement analysis, on the other hand, is to take these financial statements and other information to evaluate the company's past, current, and prospective financial position and performance for the purpose of making rational investment, credit, and similar decisions. The primary users of financial statements are equity investors and creditors. Equity investors are primarily interested in the company's l

#### Flashcard 1448738688268

Tags
#cfa-level-1 #economics #has-images #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4

Question
Both ATC and AVC take on a bowl-shaped pattern in which each curve initially declines, reaches [...] and then increases.

When output increases, average fixed cost [...]
a minimum-cost output level,

declines as AFC approaches the horizontal quantity axis.

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This shows the cost curve relationships among ATC, AVC, and AFC in the short run. The difference between ATC and AVC at any output quantity is exactly equal to the amount of AFC. Both ATC and AVC take on a bowl-shaped pattern in which each curv

#### Flashcard 1448746028300

Tags
#cfa-level-1 #economics #has-images #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4

Question
The marginal cost curve intersects both the ATC and AVC at [...] .

their respective minimum points.

This occurs at points S and T, which correspond to QAVC and QATC, respectively.

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d MC in the short run. The marginal cost curve intersects both the ATC and AVC at their respective minimum points. This occurs at points S and T, which correspond to Q AVC and Q ATC , respectively. Mathematically, when <span>marginal cost is less than average variable cost, AVC will be decreasing . The opposite occurs when MC is greater than AVC. The same relationship holds true for MC and ATC . ATC declines when MC is less than ATC. ATC increases as MC exceeds ATC

#### Flashcard 1450239462668

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Question

Total fixed cost (TFC) is the summation of all expenses that [...].

do not change when production varies

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Total fixed cost (TFC) is the summation of all expenses that do not change when production varies. It can be a sunk or unavoidable cost that a firm has to cover whether it produces anything or not, or it can be a cost that stays the same over a range of production but can change to

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Costs
rate of change in total variable cost. In Exhibit 13, TC at 5 units is 400—of which 300 is variable cost and 100 is fixed cost. At 10 units, total costs are 1,650, which is the sum of 1,550 in variable cost and 100 in fixed cost. <span>Total fixed cost (TFC) is the summation of all expenses that do not change when production varies. It can be a sunk or unavoidable cost that a firm has to cover whether it produces anything or not, or it can be a cost that stays the same over a range of production but can change to another constant level when production moves outside of that range. The latter is referred to as a quasi-fixed cost , although it remains categorized as part of TFC. Examples of fixed costs are debt service, real estate lease agreements, and rental contracts. Quasi-fixed cost examples would be certain utilities and administrative salaries that could be avoided or be lower when output is zero but would assume higher constant values over different production ranges. Normal profit is considered to be a fixed cost because it is a return required by investors on their equity capital regardless of output level. At zero output, total costs are always equal to the amount of total fixed cost that is incurred at this production point. In Exhibit 13, total fixed cost remains at 100 throughout the entire production range. Other fixed costs evolve primarily from investments in such fixed assets as real estate, production facilities, and equipment. As a firm grows in size, fixed asset expansion occurs along with a related increase in fixed cost. However, fixed cost cannot be arbitrarily cut when production declines. Regardless of the volume of output, an investment in a given level of fixed assets locks the firm into a certain amount of fixed cost that is used to finance the physical capital base, technology, and other capital assets. When a firm downsizes, the last expense to be cut is usually fixed cost. Total variable cost (TVC), which is the summation of all variable expenses, has a direct relationship with quantity. When quantity increases, total variable cost increases

#### Flashcard 1450949610764

Tags
#reestructuracion-financiera
Question
Objetivos de una reestructuración financiera

•Disminuir [...]
los costos financieros.

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Objetivos de una reestructuración financiera •Disminuir los costos financieros. •Reducir el nivel de endeudamiento. •Elevar la productividad. •Mejorar la mezcla entre recursos internos y externos. •Mejorar la posición de

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#### Flashcard 1530995543308

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#computation #social-choice
Question
An example of a function (search) problem (L P, S P, R P) in terms of graph theory is: find a nondominated vertex in a directed graph, if any. Solving the function problem on instance I ∈ L P [...] and “no solution” otherwise.
consists in outputting some S ∈ S P such that (I,S) ∈ R P , if any,

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arch) problem (L P, S P, R P ) in terms of graph theory is: find a nondominated vertex in a directed graph, if any and find all vertices with maximum outdegree are both search problems. Solving the function problem on instance I ∈ L P <span>consists in outputting some S ∈ S P such that (I,S) ∈ R P , if any, and “no solution” otherwise.<span><body><html>

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#### Annotation 1531495189772

 #bayesianism #cognitive-science #computation #computational-psychology #continue-here 2. The Basics of Bayesian Inference

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#### Annotation 1531635174668

 Jon Snow is the bastard son of Eddard Stark, Lord of Winterfell

Jon Snow - A Wiki of Ice and Fire
AC [1] Book(s) A Game of Thrones (POV)A Clash of Kings (POV)A Storm of Swords (POV)A Feast for Crows (appears)A Dance with Dragons (POV) Played by Kit Harington TV series Season 1 | Season 2 | Season 3 | Season 4 | Season 5 | Season 6 <span>Jon Snow is the bastard son of Eddard Stark, Lord of Winterfell. [2] He has five half-siblings: Robb, Sansa, Arya, Bran, and Rickon Stark. Unaware of the identity of his mother, [3] Jon was raised at Winterfell. At the age of fourteen, he joins th

#### Annotation 1531894697228

 #bayesianism #cognitive-science #computation #computational-psychology Proba- bilistic models highlight the role of prior knowledge in accounting for how people learn as much as they do from limited ob- served data and provide a framework for ex- plaining precisely how prior knowledge in- teracts with data in guiding generalization and action. They also provide a tool for ex- ploring the kinds of knowledge that people bring to learning and reasoning tasks, allow- ing us to work forwards from rational analy- ses of tasks and environments to predictions about behavior and to work backwards from subjects’ observed behavior to viable as- sumptions about the knowledge they could bring to the task. Crucially, these models do not require that the prior knowledge be innate. Bayesian inference in hierarchi- cal probabilistic models can explain how ab- stract prior knowledge may itself be learned from data and then put to use to guide learn- ing in subsequent tasks and new environ- ments.

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Question
Single Transferable Vote (STV)
STV (used, e.g., in Australia) works in stages:
• If some alternative is top for an absolute majority, then it wins.
• Otherwise, the alternative ranked at the top by the fewest voters (the plurality loser) gets eliminated from the race.
• Votes for eliminated alternatives get transferred: delete removed alternatives from ballots and “shift” rankings (i.e., if your 1st choice got eliminated, then your 2nd choice becomes 1st)

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Under plurality with runoff (and thus under STV), it may be better to abstain than to vote for your favourite alternative!

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#### Annotation 1532112538892

 Fishburn’s Classification One can classify voting rules on the basis of the information they require. The best known such classification is due to Fishburn (1977): • C1: Winners can be computed from the majority graph alone. Examples: Copeland, Slater • C2: Winners can be computed from the weighted majority graph (but not from the majority graph alone). Examples: Kemeny, Ranked-Pairs, Borda (think about it!) • C3: All other voting rules. Examples: Young, Dodgson, STV

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Fishburn’s Classification
One can classify voting rules on the basis of the information they require. The best known such classification is due to Fishburn (1977):
• C1: Winners can be computed from the majority graph alone. Examples: Copeland, Slater
• C2: Winners can be computed from the weighted majority graph (but not from the majority graph alone). Examples: Kemeny, Ranked-Pairs, Borda (think about it!)
• C3: All other voting rules. Examples: Young, Dodgson, STV

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Fishburn’s Classification One can classify voting rules on the basis of the information they require. The best known such classification is due to Fishburn (1977): • C1: Winners can be computed from the majority graph alone. Examples: Copeland, Slater • C2: Winners can be computed from the weighted majority graph (but not from the majority graph alone). Examples: Kemeny, Ranked-Pairs, Borda (think about it!) • C3: All other voting rules. Examples: Young, Dodgson, STV

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Question
Give an example of Fishburn's category of voting rules C1:
Examples: Copeland, Slater

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Fishburn’s Classification One can classify voting rules on the basis of the information they require. The best known such classification is due to Fishburn (1977): • C1: Winners can be computed from the majority graph alone. Examples: Copeland, Slater • C2: Winners can be computed from the weighted majority graph (but not from the majority graph al

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#### Flashcard 1532121189644

Question
Give an example of Fishburn's category of voting rules C2.
Examples: Kemeny, Ranked-Pairs, Borda (think about it!)

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lassification is due to Fishburn (1977): • C1: Winners can be computed from the majority graph alone. Examples: Copeland, Slater • C2: Winners can be computed from the weighted majority graph (but not from the majority graph alone). <span>Examples: Kemeny, Ranked-Pairs, Borda (think about it!) • C3: All other voting rules. Examples: Young, Dodgson, STV<span><body><html>

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Question
Give an example of Fishburn's category of voting rules C3.
Examples: Young, Dodgson, STV

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ty graph alone. Examples: Copeland, Slater • C2: Winners can be computed from the weighted majority graph (but not from the majority graph alone). Examples: Kemeny, Ranked-Pairs, Borda (think about it!) • C3: All other voting rules. <span>Examples: Young, Dodgson, STV<span><body><html>

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#### Annotation 1532128267532

 F is anonymous if F (R 1 , . . . , R n ) = F (R π(1) , . . . , R π(n) ) for any profile (R 1 , . . . , R n ) and any permutation π : N → N.

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F is anonymous if [...] for any profile (R 1 , . . . , R n ) and any permutation π : N → N.
F (R 1 , . . . , R n ) = F (R π(1) , . . . , R π(n) )

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F is anonymous if F (R 1 , . . . , R n ) = F (R π(1 ) , . . . , R π(n) ) for any profile (R 1 , . . . , R n ) and any permutation π : N → N.

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#### Annotation 1532132986124

 F is neutral if F (π(R)) = π(F (R)) for any profile R and any permutation π : X → X (with π extended to profiles and sets of alternatives in the natural manner).

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Question
F is neutral if [...] for any profile R and any permutation π : X → X (with π extended to profiles and sets of alternatives in the natural manner).
F (π(R)) = π(F (R))

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F is neutral if F (π(R)) = π(F (R)) for any profile R and any permutation π : X → X (with π extended to profiles and sets of alternatives in the natural manner).

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#### Annotation 1532136393996

 F is positively responsive if $$x^*\in F(R)$$ implies $$\{x^*\}=F(R')$$ for any alternative $$x^*$$ and any two distinct profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus \{x^*\}$$

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Question
F is positively responsive if [...] for any alternative $$x^*$$ and any two distinct profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus \{x^*\}$$
$$x^*\in F(R)$$ implies $$\{x^*\}=F(R')$$

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F is positively responsive if $$x^*\in F(R)$$ implies $$\{x^*\}=F(R')$$ for any alternative $$x^*$$ and any two distinct profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\se #### Original toplevel document (pdf) cannot see any pdfs #### Flashcard 1532145831180 Question May's Theorem Answer A voting rule for two alternatives satisfies anonymity, neutrality, and positive responsiveness if and only if that rule is the simple majority rule. status measured difficulty not learned 37% [default] 0 #### pdf cannot see any pdfs #### Flashcard 1532150811916 Tags #chracterization #computation #social-choice #voting-rules Question F satisfies reinforcement if, whenever Answer we split the electorate into two groups and some alternative were to win for both groups, then it will also win for the full electorate. status measured difficulty not learned 37% [default] 0 #### pdf cannot see any pdfs #### Flashcard 1532153171212 Tags #chracterization #computation #social-choice #voting-rules Question What is the axiom of continuity? Answer For two subelectorates X,Y if x wins in X and y wins in Y and x is the general winner in \(X\cup Y$$, it must be possible to add copies of Y to the electorate until y becomes the general winner.

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#### Annotation 1532155530508

 #chracterization #computation #social-choice #voting-rules Young showed that F is a (generalised) positional scoring rule iff it satisfies anonymity , neutrality, reinforcement, and a technical condition known as continuity.

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Young's Theorem states that F is a [...] iff it satisfies anonymity , neutrality, reinforcement, and a technical condition known as continuity.
(generalised) positional scoring rule

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Young showed that F is a (generalised) positional scoring rule iff it satisfies anonymity , neutrality, reinforcement, and a technical condition known as continuity.

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#### Annotation 1532160249100

 #chracterization #computation #social-choice #voting-rules Condorcet Jury Theorem: Suppose a jury of n voters need to select the better of two alternatives and each voter independently makes the correct decision with the same probability p > 1/2 . Then the probability that the simple majority rule returns the correct decision increases monotonically in n and approaches 1 as n goes to infinity.

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Condorcet Jury Theorem: Suppose a jury of n voters need to select the better of two alternatives and each voter independently makes the correct decision with the same probability p > 1/2 . [...]
Then the probability that the simple majority rule returns the correct decision increases monotonically in n and approaches 1 as n goes to infinity.

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Condorcet Jury Theorem: Suppose a jury of n voters need to select the better of two alternatives and each voter independently makes the correct decision with the same probability p > 1/2 . Then the probability that the simple majority rule returns the correct decision increases monotonically in n and approaches 1 as n goes to infinity.

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#### Annotation 1532164967692

 #chracterization #computation #social-choice #voting-rules Borda Rule as Maximum Likelihood Estimator: If each voter independently ranks the true winner out of m alternatives at position k with probability $$\frac{2 m−k} {2 m −1}$$ , then the maximum likelihood estimator is the Borda rule.

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Borda Rule as Maximum Likelihood Estimator: If each voter independently ranks the true winner out of m alternatives at position k with probability [...] , then the maximum likelihood estimator is the Borda rule.
$$\frac{2^{m−k}} {2^{m −1}}$$

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Borda Rule as Maximum Likelihood Estimator: If each voter independently ranks the true winner out of m alternatives at position k with probability $$\frac{2 m−k} {2 m −1}$$ , then the maximum likelihood estimator is the Borda rule.

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Tags
#chracterization #computation #social-choice #voting-rules
Question
consensus profiles
profiles in which there is a clear (set of) winner(s).

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#### Annotation 1532175191308

 #chracterization #computation #social-choice #voting-rules Order correctly by restrictiveness: 1 Majority Winner : there exists an alternative x that is ranked first by an absolute majority of the voters (; x wins) 2 Unanimous Winner : there exists an alternative x that is ranked first by all voters (; x wins) 3 Condorcet Winner: there exists a Condorcet winner x (; x wins) 4 Unanimous Ranking : all voters report exactly the same ranking (; the top alternative in that unanimous ranking wins)

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Order correctly by restrictiveness:

1 Majority Winner : there exists an alternative x that is ranked first by an absolute majority of the voters (; x wins)
2 Unanimous Winner : there exists an alternative x that is ranked first by all voters (; x wins)
3 Condorcet Winner: there exists a Condorcet winner x (; x wins)
4 Unanimous Ranking : all voters report exactly the same ranking (; the top alternative in that unanimous ranking wins)
$$3\supseteq 1 \supseteq 2 \supseteq 4$$

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Order correctly by restrictiveness: 1 Majority Winner : there exists an alternative x that is ranked first by an absolute majority of the voters (; x wins) 2 Unanimous Winner : there exists an alternative x that is ranked first by all voters (; x wins) 3 Condorcet Winner: there exists a Condorcet winner x (; x wins) 4 Unanimous Ranking : all voters report exactly the same ranking (; the top alternative in that unanimous ranking wins)

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Which notion of distance is defined by the following formula: $$\frac {1}{2} \sum_{i\in N} \#\{(x,y)\in X^2:1_{i\in N^R_{x\succ y}} \neq 1_{i\in N^{R'}_{x\succ y}}\}$$
Swap distance: minimal number of pairs of adjacent alternatives that need to get swapped to get from R to R' .

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Tags
#chracterization #computation #social-choice #voting-rules
Question
How is discrete distance defined?
Number of voters for which the two profiles diverge: $$\#\{i\in N: R_i\neq R'_i \}$$

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Tags
#chracterization #computation #social-choice #voting-rules
Question
Condorcet Winner + Swap Distance characterizes...
Dodgson Rule

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#chracterization #computation #social-choice #voting-rules
Question
Kemeny Rule is chracterized by ...
Unanimous Ranking + Swap Distance

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#chracterization #computation #social-choice #voting-rules
Question
Borda is characterised by
the unanimous winner consensus criterion and the swap distance.

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#chracterization #computation #social-choice #voting-rules
Question
Plurality is characterised by
the unanimous winner consensus criterion and the discrete distance

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#computation #social-choice #voting-rules
Question
What axiom is expressed by the following intuition? If x and y are identical states, except that in x I paint my bedroom white, while in y I paint it pink, then I should be able to dictate the relative social ranking of x and y.
Liberalism

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#computation #social-choice #voting-rules
Question
F is called liberal if, for every individual i ∈ N , there exist two distinct alternatives x, y ∈ X such that i is two-way decisive on x and y :
$$i\in N^R_{x\succ y}$$ implies $$y\notin F(R)$$ and $$i\in N^R_{y\succ x}$$ implies $$x\notin F(R)$$

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#computation #social-choice #voting-rules
Question
For |N| $$\geq$$ 2, there exists no social choice function that is both Paretian and liberal.

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#### Annotation 1532207697164

 #computation #social-choice #voting-rules F is called weakly monotonic if $$x^*= F(R)$$ implies $$x^*= F(R')$$ for any alternative x* and any two profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus\{x^*\}$$

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Tags
#computation #social-choice #voting-rules
Question
F is called weakly monotonic if $$x^*= F(R)$$ implies $$x^*= F(R')$$ for any alternative x* and any two profiles R and R' with [...]
$$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus\{x^*\}$$

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F is called weakly monotonic if $$x^*= F(R)$$ implies $$x^*= F(R')$$ for any alternative x* and any two profiles R and R' with $$N^R_{x\succ y}\subseteq N^{R'}_{x\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus\{x^*\}$$

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Tags
#computation #social-choice #voting-rules
Question
F is called strongly monotonic if
$$x^*= F(R)$$ implies $$x^*= F(R')$$ for any alternative x* and any two profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ for all $$y \in X\setminus\{x^*\}$$

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F is called weakly monotonic if $$x^*= F(R)$$ implies $$x^*= F(R')$$ for any alternative x* and any two profiles R and R' with $$N^R_{x^*\succ y}\subseteq N^{R'}_{x^*\succ y}$$ and $$N^R_{y\succ z}= N^{R'}_{y\succ z}$$ for all $$y,z\in X\setminus\{x^*\}$$

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Tags
#computation #social-choice #voting-rules
Question
Intuition for weak monotonicity =
raising the winner preserves the winner

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#computation #social-choice #voting-rules
Question
What axiom characterisizes the following intuition: lowering a loser preserves the winner
strong monotonicity

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#computation #social-choice #voting-rules
Question
a resolute SCF F is called surjective (or nonimposed ) if
for every alternative x ∈ X there exists a profile R such that F (R) = x.

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#computation #social-choice #voting-rules
Question
Muller Satterthwaite Theorem: Any resolute SCF for $$\geq$$ 3 alternatives that is surjective and strongly monotonic...
is a dictatorship

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#### Annotation 1532291058956

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 1 Introduction

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 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 2 Preliminaries: KB-Models and Belief-Knowledge Logic

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#### Annotation 1532317011212

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 4 Conditional Doxastic Models

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#### Annotation 1532319370508

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 5 Dynamic Belief Revision: Public Announcements

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#### Annotation 1532321729804

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 6 Private Announcements to subgroups

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#### Annotation 1532324089100

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 7 Conclusion

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#### Annotation 1532326972684

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #section #serious-possibility-paradox-project 3 A semantic, multi-agent, epistemic AGM theory

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#### Annotation 1532329331980

 #abstract #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project Abstract In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM’s, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM’s. Moving then to belief updates (sometimes called “dynamic” belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of age nts. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM’s, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a “cheating version” of the Muddy Children Puzzle. Key words: belief revision, belief update, conditional belief, dynamic epistemic logic, public announcement, modal logic, multi-agent system

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#### Annotation 1532331691276

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project Once upon a time there were three very wise children, playing in a garden, under the tall trees. Despite their father’s warning, naughty Adam and Eve got mud on their foreheads, but obedient Mary stayed clean. Then the father came to them and said:“Behold, at least one of you is dirty”. Eve secretly checks her face in a mirror and answers correctly: "I'm dirty". How will Adam and Mary answer if they suspect no cheating?

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Tags
#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #muddy-children #private-announcements #public-announcements #serious-possibility-paradox-project
Question
Once upon a time there were three very wise children, playing in a garden, under the tall trees. Despite their father’s warning, naughty Adam and Eve got mud on their foreheads, but obedient Mary stayed clean. Then the father came to them and said:“Behold, at least one of you is dirty”. Eve secretly checks her face in a mirror and answers correctly: "I'm dirty". How will Adam and Mary answer if they suspect no cheating?
Eve: goes crazy, incoherent (believes both that she is clean and that she is dirty)

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Once upon a time there were three very wise children, playing in a garden, under the tall trees. Despite their father’s warning, naughty Adam and Eve got mud on their foreheads, but obedient Mary stayed clean. Then the father came to them and said:“Behold, at least one of you is dirty”. Eve secretly checks her face in a mirror and answers correctly: "I'm dirty". How will Adam and Mary answer if they suspect no cheating?

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#### Annotation 1532336409868

 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project A knowledge-belief frame (KB-frame for short, see e.g. [17], pg. 89) is a Kripke frame of the form (S, → a , ∼ a ) a∈A , with a given set of states S and two binary relations for each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.

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Tags
#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
A knowledge-belief frame (KB-frame for short, see e.g. [17], pg. 89) is a Kripke frame of the form (S, → a , ∼ a ) a∈A , with a given set of states S and two binary relations for each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) [...] (3) if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.
if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w;

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or each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) <span>if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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#### Flashcard 1532341914892

Tags
#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
A knowledge-belief frame (KB-frame for short, see e.g. [17], pg. 89) is a Kripke frame of the form (S, → a , ∼ a ) a∈A , with a given set of states S and two binary relations for each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) [...] (4) for every s ∈ S there e xists some t ∈ S such that s → a t.
if s → a t then s ∼ a t ;

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ile the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) <span>if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
A knowledge-belief frame (KB-frame for short, see e.g. [17], pg. 89) is a Kripke frame of the form (S, → a , ∼ a ) a∈A , with a given set of states S and two binary relations for each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) [...]
for every s ∈ S there e xists some t ∈ S such that s → a t.

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beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) <span>for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
For a KB fram (S, a, a) what condition on the knowledge operator does the following correspond to? if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w;
Full introspection of knowledge and belief.

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or each agent; the first relation ∼ a is meant to capture the knowledge of agent a, while the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) <span>if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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#### Flashcard 1532346895628

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
For a KB fram (S, a, a) what condition on the knowledge operator does the following correspond to? If s → a t then s ∼ a t ;
Knowledge implies Belief

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ile the second → a captures his beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) <span>if s → a t then s ∼ a t ; (4) for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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#### Flashcard 1532349254924

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
For a KB fram (S, a, a) what condition on the knowledge operator does the following correspond to? For every s ∈ S there e xists some t ∈ S such that s → a t.
Consistency of Belief

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beliefs. A KB frame is required to satisfy the following natural conditions: (1) each ∼ a is reflexive: s ∼ a s; (2) if s ∼ a t then we have: s → a w iff t → a w, and also s ∼ a w iff t ∼ a w; (3) if s → a t then s ∼ a t ; (4) <span>for every s ∈ S there e xists some t ∈ S such that s → a t.<span><body><html>

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 #conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project The maps • a and •(a) are called appearance maps: s a is the doxastic appearance of s to a (or the theory of a about s), and s(a) is the epistemic appearance of s to a (or the knowledge of a about s). The equivalence between the two definitions of knowledge-belief models is easily verified

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
s a is the doxastic appearance of s to a (or the theory of a about s). Define it formally.
$$s_a:S\rightarrow 2^S$$, where $$s_a=\{t: s\rightarrow_a t\}$$

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The maps • a and •(a) are called appearance maps: s a is the doxastic appearance of s to a (or the theory of a about s), and s(a) is the epistemic appearance of s to a (or the knowledge of a about s). The equivalence between the two definitions of knowledge-belief models is easily verified<

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#### Flashcard 1532356332812

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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project
Question
Let s a be the doxastic appearance of s to an agent a, $$P\subseteq S$$ a proposition and Ba the belief operator for a. Define the proposition BaP in temrs of sa.