8 Voting

Question 1

Voting

Answer 1

Voting is a mechanism that chooses the outcome of a negotiation based on the inputs (votes) given by all agents to a set of competing opinions.

Question 2

Arrows impossibility theorem

Answer 2

Social choice rule: it creates an ordering of the group of alternatives, so that the most (socially) preferred alternative is chosen.

Theorem: No social choice rule satisfies all of these conditions: (calculability, completeness, linearity, no dictatorship, pareto efficiency, neutrality)

Question 3

Voting mechanisms

Answer 3

BASIC PROTOCOLS

• Plurality
• Anti-Plularity
• Best-worst
• Approval

PROTOCOLS BASES ON TOTAL ORDERS

• Binary
• Borda
• Condorcet

COMPLEX PROTOCOLS

• Linguistic votes
• Uncertain opinions

Question 4

• Plurality

Answer 4

Each agent can give 1 vote to the best alternative
The alternative with the highest number of votes wins

(most simple, computationally most efficient, equality principle 1 agent = 1 vote)
(problems: huge effect of irrelevant alternatives, strange effects)

Question 5

• Anti-Plularity

Answer 5

Each agent gives a negative vote to the worst alternative

The alternative with the lowest number of votes wins

Question 6

• Best-worst

Answer 6

Each agent gives a negative to the worst and a positive vote to the best alternative
The alternative with more points wins

Question 7

• Approval

Answer 7

Each voter selects a subset of candidates (k-approval voting)
The candidates with most votes wins

Question 8

• Binary

Answer 8

All options are ordered and then evaluated in pairs ( 1 &2 , the winner with 3, the winner with 4 and so on). The option that wins the last comparison is the overall winner.

Problem: The order of the pairings affects the outcome. The last options have more chances of winning. An alternative might win even if there is another alternative that is preferred by all agents.

Question 9

• Borda

Answer 9

For each voter we assign |#_of_voters| points to the preferred option, |#_of_voters|-1 points to the second and so on. The points are added across the voters and the alternative with the highest count wins.

Problem: Most computationally expensive.
Borda-paradox and Inverted-order-paradox: Eliminating or adding one irrelevant alternative may totally change the outcome.

Question 10

• Condorcet

Answer 10

Each voter ranks the candidates in order of preference
Each candidate is compared to each other. If a candidate wins all comparisons he is the winner of the election

Problem: circular ambiguities are possible: no alternative wins