4: Social Choice Theory: Two Options

Question 1

What does Condorcets Jury Theorem state?

Answer 1

{voting for information gathering}

if every voter is independently correct with p>0.5, the probability of correct judgement using majority rule aproaches 1 as n→∞ (quickly)

Question 2

What does Mays Theorem state?

Answer 2

{voting to derive a social preference}

Majority voting is the only SWF that satisfies
1. symmetry among agents
2. neutrality between alternatives
3. positive responsiveneess

Question 3

What does symmetry among candidates mean?

Answer 3

If the candidates are permutated,the result remains the same

Question 4

What does neutrality between alternatives mean?

Answer 4

If the alternatives are switched, the result is switched

Question 5

What does positive responsivenis mean?

Answer 5

If every single one prefers a over b, the SWF will choose a over b