Group Choice: Social Choice, Condorcet, Intrasitivity Flashcards
(20 cards)
5 criticisms of rational choice
- Ideology
– Pretends to be objective and ignores that it is value-laden - Formality
– Problems with deductive reasoning; completeness and transitivity are not necessary, preferences cannot be observed (only choices) - Empirical
– Lack of explanatory and predictive power - Ethical
– Justifying immoral behavior by arguing it is rational - Scope
– Ignores factors in behavior and thereby neglect the influence of the environment
What is social choice theory?
Framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare
- Move from individual choice to group choice analysis
Examples of questions for social choice theory
- How do we combine our votes to points towards a winner?
- If we have a jury system, how do we combine the jury votes to come up with an ultimate judgement?
- How do we decide upon a vacation activity among a group of friends?
- How do we choose a restaurant if we have different preferences among our group of friends?
What does social choice theory often blend?
SCT often blends voting theory with elements of welfare economics
Why is social choice theory seen as pessimistic?
- Rationality at the individual does not always translate into rationality at the group level
- Group choices often depend on rules and regulations
– Altering rules and regulations often leads to an entirely different result
What does the idea that individual rationality does not always translate to group rationality imply?
This has severed implications for our understanding of democracy (is it really as good as we think?), the role of voting (is it really as important as we think?)
What initial problem can we run into when trying to make group decisions? (3 people, 3 choices)
- Individuals may not unanimously share first preference
– There is not majority found among 1st preferences
What is a solution to the problem of not sharing a first preference?
Round-robin tournament (pair(ed) comparison)
What is a round-robin tournament?
Each alternative is pitted against each other alternative and, if one is preferred by the majority to all the others, then it is declared the group choice
What are the possible ways of producing a solution in group decision making?
- Unanimously voting
- Majority rule
- Round-robin tournament
What are assumptions made about group decision making (eg for round-robin tournaments)?
- Individuals are honest, they will reveal their sincere preferences
– Individuals can, of course, vote strategic
What is cyclic majority?
Although each individual preference is complete and transitive: group preference relations are sometimes cyclical
- Group preference order is intransitive
- A different majority coalition supporting the winner in each pairwise comparison
When is cyclic majority likely to happen?
It is likely to occur when a group must make a choice
- Elections
- Legislatures
- Cabinets
What is another term for a cyclic majoirty?
Condorcet paradox
What is the Condorcet paradox?
Group preferences can be cyclic even if the preferences of the individual voters are rational
Nicholas de Condorcet facts
- Nicholas de Condorcet (1743-1794)
- French philosopher and mathematician
- First that applied mathematics in social sciences
- He was working for the government
- Enlightenment: feminist, reforms of criminal laws, laissez-faire economics
- Very active in the French Revolution
- Was branded as a traitor due to his criticism on the new French constitution
- Found dead in prison and his remains are lost
What is a Condorcet winner?
If an alternative beats all other alternatives in pairwise comparison, then this alternative is a Condorcet Winner
What does it mean if there is a Condorcet winner?
If there is a Condorcet winner, then group preferences are not cyclical and there is an outcome that is “truly” preferred by a majority
How often do cyclic majorities occur (in the case of {x,y,z} {A,B,C})?
- 12 from 216 possibilities generate Condorcet paradox
- 204 from 216 possibilities generate Condorcet winner
How can P(Condorcet paradox) increase?
- The number of individuals
- The number of alternatives
– Especially when the number of alternatives increases, the occurrence of cycles becomes nearly certain
This is especially problematic in the realm of politics
