Condorcet jury Flashcards
What is the probability that a 3 persona jury with signal of quality q, comes to the right decision?
P(correct) = 3q^2(1-q) +q^3
What is the collective choice function?
Let C(P) = P -> x be the collective choice function, where P = (p1, p2,..,pn) are strict orderings (not preferences)
What makes a collective choice function pareto efficient?
C(P) is pareto efficient if whenever x ε X is the best alternative for everyone then C(P) = x
What makes a collective choice function monotonic?
C(P) is monotonic if whenever C(P) = x and for all iεN and all y ε X, xPi’y if xpi’y, then C(P’) = x
Given an ordering, x gets chosen by the collective choice function, if you change the orderings such that x either goes up or stays the same in the rankings of all agents, the collective choice function still chooses x.
What makes a choice function dictatorial?
C(P) is dictatorial is there exists an i ε N such that C(P) = x if and only if C(pi) = x
What makes a choice function onto?
C(P) is onto if every alternative is chosen for some profile.
What makes a choice function strategy proof?
If an agent can change the decision made by the collective choice function, he does not have the incentive to do so. Also, if I can manipulate the outcome of the collective choice, I do not want to
What is the dictator theorem in collective choice theorem?
If abs X >= 3 and C is pareto efficient and monotonic then C is dictatorial
How do you know if a choice function is pareto efficient and monotonic?
If c is onto and strategy proof, then it is Pareto efficient and monotonic.
What is the Gibbard-Satterthwaite theorem in collective choice?
If absX >=3 and C is onto and strategy proof, then it is dictatorial
What is the condorcet jury theorem?
As the number of Jurors converges to infinity, the majority rule selects the best alternative with probability 1.
