rational choice theory | Quizlet

social choice theory

a theoretical framework for analaysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare

public choice theory

the study of political decision making with the help of economic models. it models individual behavior under a variety of political institutions

expected utility theory

the account of how to choose rationally when you are not sure which outcome will results from you acts.

game theory

the study of mathematical models of strategic interaction between rational decisionmakers

a priori assumptions

result in deductive models of political behavior. for RC two important ones: methdological individualism & rational choice behavior (utility maximization)

building blocks of RC

methodological individualism & rational choice behavior (utility maximization)

methodological individualism

the unit if analysis is the individual person. even group actions are explained by the actions of individuals. Bottom up analysis

society in RC

society is the sum of individuals. society does not shape indivivduals, individuals are shaped independently of the social structure

bottom up analysis

every analysis must begin with the individuals, deal with individual choices and experiences, with collective fromed as aggregates.

Rationality

individuals has goals or desires & individuals act in accordance with those goals and desires.

preferences

individuals goals/desires. we don't care where these come from and they will not change much in the short run. We only know our own preferences, but we make assumptions about the preferences of others

self-interested

when a person is rational. does not mean selfish

thin version of rationality

we do not make any assumptions about an individual's goal. we only know s/he has goals

thick version of rationality

we make more explicit assumptions about the goals of individuals.

p

prefers

I

indifferent

a choice is rational when

the object chosen is better or as good as any other available objects according to the chooser's preference

an individual is rational when

if s/he makes a choice between the outcomes that is in line with his or her prefernces

two assumptions for preference ordering

Comparability/completeness & Transitivity

comparability / completeness

All alternatives in the choice set must be comparable in terms of preferences. the outcomes are comparable if, for any pair of them, you can indicate whether you prefer the first to the second etc.

transitivity

A strict preference relation is said to be transitive if for any of the three possibilities x Pi Y, y Pi z, x Pi z. If i prefer x over y and y over z, then i should prefer x over z

problems with completeness

if the comparison does not make sense for the individual. if the individual does not always see options as competing alternatives

problems with transitivity

it requires consistency, it get complicated when stakes are very low and uncertainty is high

cost-benefit calculation

a rational individual would pursue a goal if the benefits gained from that goal outweigh the costs.

belief

a probability statement relating the effectiveness of a specific action (or instrument) for achieving various outcomes.

benefits

the preference that will be satisfied

costs

the resources that are needed when taking the action

instrumental rationality

a rational individual will choose the action s/he believes will lead to the most preferred outcome

certainty

the relationship between action and outcome is clear.

risk

the relationship between action and outcome is unclear, but it is possible to link its probabilities

uncertainty

the relationship between action and outcome is imprecise and entirely unclear

utility

the benefit the individual derives from the outcome

formal terms of utility

a utility function U(x) assigns a numerical value to each element in choice set, X, ranking the elements of X in accordance with the individual's preferences

two types of utility

ordinal utility & cardinal utility

ordinal utility

assign a number to each outcome of the preference ordering to denote its rank in the individual's preference order. Only captures the ranking of preferences.

problem with ordinal utility

the results of some actions may be risky or uncertain. And actions often entail costs. With ordinal ranking we cannot discuss the change in utilities

cardinal utility

tells us how much an individual prefers one outcome to another. we can discuss the change in utilities. it expresses the intensity of preferences for a given outcome. we cannot compare the cardinal utilities of two persons, or make interpersonal comparisons.

the intensity of preferences is relative to

the individual, the set of outcomes

rationality and utility

a preference relation can be represented by a utility function only if it is rational.

utility in political setting

most prominently voting

ordinal voting methods

ranking ballots by marking a circle

cardinal voting methods

ranking bellots by giving a rate between -10 and 10

Single Transferable vote

ordinal voting system. number the candidates on a ballot from most to least preferred. a candidate must reach a set amount of votes (quotas). First only 1st preference is counted, anyone who reached the quota is elected. if more votes than quota than these are transferred to the second preference. Least preferred candidate is eliminated and his/her votes are transferred to others.

lotteries

lotteries assign probabilities to outcomes. individuals have an expected utility from each lottery.

two conditions for lotteries

all probabilities must be between 0 and 1 & all probabilities must sum up to 1

a rational choice in lotterries

the one that received the highest value according to the principle of expected utility, being this the sum of the products of probability and utility over all possible outcomes.

expected utility theory

Daniel Bernouille, John von Neumann and Oskar Morgenstein. the theory deals with situations in which indiviuals need to decide without knowing which outcomes may result from that decision.

expected utility calculation

probability of the action x cardinal utility - costs

assumptions about preferences over lotteries

we assume preferences over lotteries are complete and transitive, and we assume people are indifferent between lotteries that yield the same probabilities and outcomes.

risk acceptant

(payoff)2

risk averse

wortel(payoff)

5 types of criticism

1. ideology

2. formality

3. empirical

4. ethical

5. scope

social choice theory

framework for analysis of combining individual opinions, preferences, interest, or welfare to reach a collective decision or social welfare

criticism that SCT is a pessimistic theory

rationality at the individual does not always translate into ratinoality at the group level. Group choices often depend on rules and regulations

round robin tournament

a potential solution when there is no unanimously shared first preference. Each alternative is pitted against another alternative and, if one is preferred by the majority to all the other, then it is declared the group choice.

several ways of producing a solution in SCT

unanimously voting, majority rule, round-robin tournament

assumptions SCT

individuals are honest, they will reveal their sincere preferences & individual can vote strategic

cyclic majority

although each individual preference is complete and transitive, group preference relations in sometimes cyclical. group preference order is intransitive. A different majority coalition supporting the winner in each pairwise comparison

condorcet paradox

group preferences can be cyclic even if the preferences of the individual voters are rational.

condorcet winner

if an alternative can beat all other alternatives in pairwise comparisons, then this alternative is a Condorcet winner, the paradox is solved. If there is a winner, then group preferences are not cyclical and there is an outcome that is 'truly' preferred by a majority.

condorcet paradox increase with

especially number of alternatives, and number of individuals

arrow

main contributor to social theory. Arrow's imposibility theorem

social welfare function

finite set of of at least three different policy options. everyone has preferences over the policy options, which are complete and transitive. Translates individual preferences to a group preference.

object of Arrow

find one outcome (the social maximum) in a political democracy that is consistent with the preferences of all individuals in a society.

conditions of Arrow

1. universal adminssibility

2. pareto optimality or unanimity

3. independence from irrelevant alternatives

4. non-dictatorship

impossibility thoery

Arrow. The only way of satisfying U, P, and I is a dictatorship.

condition u

universal admissibility. Each individual from a group may adopt any strong or weak complete and transitive preference orderings over the alternatives. We do not want to restrict the choice of an individual in any manner, they can choose whatever they want as long it is rational.

condition P

Pareto optimality or Unanimity, value laden condition. If every individual of the groups prefer A to B, the the group preference must also be A to B. Ensures the group choice is responsive to the individual preferences.

condition I

Independence of Irrelevant Alternatives. If A is preferred to B out of a choice set, introducing a third option X, must not make B preferable to A.

condition D

non-dictatorship. There is no distinguished individual who dictates the group preference, no matter what the preferences are of the other member of the group. This is a minimal fairness condition.

dictatorship

a dictator is a person whose individual preferences coincide with the social ones. a person that turn out to be the winning on all sides. A pivotal voter.

Arrow's conclusion

the conditions cannot be satisied simultenously. any SWF which respects transitivity and completeness, unanimity, and independece of irrelevant alternatives is a dictatorship.

Arrows implications

the only way to obtain a rational group preference all the time is by relaxing one of these condition. Arrow's theorem is probalistic, you may get a coherent group choice, but you cannot guarantee it. There is a tradeof between group rationality and the concentration of decision making power.

escape routes Arrow

ways of solving the impossibility, or reducing its likelihood:

1. move beyond yes/no votes or beyond ranking, maybe include cardinal utility.

2. consensus systems, no voting but discussion

3. restricting UD; limit choices

kenneth may

special case of Arrow's conditions. Applied to simple majority-rule group decision processes. May's theorem deals with special case of social choice between just two alternatives.

method of majority rule

Kenneth May. for any pair of alternatives, j and k, j is preferred by the grou pto k, if and only if the number of group members who prefer j to k exceeds the number o group members who prefer k to j

conditions of May

1. universal domain

2. anonymity

3. neutrality

4. monotinicity

Condition U (May)

Universal domain. each individual from a group may adopt any strong or weak complete and transitive preference orderings over the alternatives.

condition A (May)

Anonimity. social preferences depend only on the collection of individual preferences, not on who has which preferences. each individual is treated equally and identically.

condition N (May)

neutrality. interchanging the ranks of alternatives j and k in each individual's preference ordering has the effect of interchanging the ranks of j and k in the group's preference ordering

condition M (May)

Monotonicity. If an alternative j beats or ties with another alternative k and j rises in some group member's preference from below to k to the same or higher rank thatn k, then j now strictly beats k.

May's theorem

a method of preference aggregation over a pair of alternatives (2) satisfies conditions U, A, N, and M, only if it is MMR.

duncan black

invented the most famous universal domain restriction: Single peakedness. A solution to the condorcet paradox. social choice theorist

a group of agents is said to have single-peaked-preferences if:

1. each agent has an ideal choice set

2. for each agent, outcomes that are furhter from his ideal choice are preferred less.

moving left of right from favorite alternative

utility goes down

condrocet and spatial modelling

condorcet cycles cannot occur when individual preferences are single peaked. Single-peakedness as a domain restriction, removes the occurence of Condorcet cycles.

Black's Theorem

if there is an odd number of votes that display single-peaked preferences, then a condorcet winner exists. By restricting Condition UD, we can prove that the condorcet paradox will never arise.

bliss points

voters' most preferred outcomes

median motion

if all voters have single-peaked curves as preferences, then the median motion will be adopted by the committee

median

seperates a set of numbers into two halves, with one half (50%) falling above the median and the other half (50%) falling below the median.

median preference

the preference preferred by the majority

Black's median voter theorem

when preferences are single peaked, majority rule preferences are transitive and the feasible alternative which lies highest on the preferences o the median voter is majority winner (or Condorcet winner). When preferences aer single-peaked, the ideal point of the median voter is the majority preference.

Hotellling's model

Black's median voter theorem is a formalization of the Hotelling's model of Anthony Down

formalization of Hotellings model, median voter theorem

if

1. we can order alternatives along a single dimensions, and

2. preference orderings are single-peaked along this dimension, then...

there is a identifiable majority preference, this is the preference of the median voters.

the ideal point of the median voters has an empty winset.

empty winset

there are not alternatives that can beat the ideal point. In case of cyclic majority, the winset is not empty.

assumptions median voter theorem

- full participation is assumed

- they participate sincerely

- politician's lack ideological convictions, which could lead them to position themselves away from the median voter.

- assumes perfect information along three dimensions: voter knowledge of the issues; politician knowledge of the issues; and politician knowledge of voter preference.

- there is only one single dimension that plays a role

theorists that deal with mutlidimensionality

Plott & McKelvey

Plott's theorem

if members of a group have circular indifference curves, and if their ideal points are distributed in radically summetric fasion around the ideal point x, then the winster of x is empty.

plott: basic parameters

- the smaller the circle, the higher the utility

- the ideal point is in the middle, that is the most preferred otucome.

- if an individual's indifference curves are circular, then s/he always prefers points taht are closer to those further away

- all points inside the circle, being closer to the ideal, are actually preferred by the individual oto the one on the line

Radially symmetric fasion

- element of Plott

- the policy space is effectively one-dimensional

- the voters on each side of the median have directly opposing interests which cancel them out.

- a multidimensional space become one-dimensional