Handling preferences of multiple players

Question 1

Type of preferences.

Answer 1

• Individual preferences
• Group preferences

Question 2

What does “information mashup” mean in voting theory?

Answer 2

…

Question 3

Definition of SOCIAL WALFARE FUNCTION.

Answer 3

• Set of players N
• Set of alternatives (outcomes) A
• Players have preferences over them
• Goal of the social function
• Linear order outcomes
• …

f: R(A)^n -> R(A)

Question 4

Properties of the social walfare function.

Answer 4

• Can be PARETO EFFICIENT
• Can satisfy “Indipendence of Irrilevant Alternatives” (IIA)
• Can be DICTATORSHIP
• Can be MONOTONIC
• Can satisfy “non-imposition”: all the possibile outcomes can be reached

Question 5

Arrow’s theorem.

Answer 5

Any f over A >= 3 that is Pareto efficient and IIA is dictatorial.

Question 6

What is democracy?

Answer 6

Majority rule.

Question 7

Types of voting.

Answer 7

• Plurality voting: sorting outcomes (elimination procedure for ties) -> select the outcome which have most 1st positions in the rankings
• Borda count: giving a vote to each outcome -> trivial
• Approval voting: voting for multiple (M) outcomes (1 point for each choice) -> trivial
• Cumulative voting: people can distribute a fixed number of votes -> trivial

A specific type of vote can resolves paradoxes.

Question 8

Definition of CONDORCED CYCLES.

Answer 8

Collective preferences can be cyclic, even if the preferences of individual voters are not cyclic.

This is paradoxical, because it means that majority wishes can be in conflict with each other.

Question 9

What is a CONDORCED WINNER.

Answer 9

The outcome using the majority rule.

If we don’t have a condorced winner we have the Condorced paradox.

Question 10

Interesting property of the Condorced cycles.

Answer 10

The probability of Condorcet cyles grows with the number of candidates.