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Voting Rules: What’s Fair?

Voting Rules: What’s Fair?. Q. What is the most fair voting rule? Suppose three proposals to spend $15: Z=Status Quo (currently, we spend $10 on guns and $5 on butter) X= Proposal (peaceniks want to spend $5 on guns and $10 on butter)

geoffrey-kristian
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Voting Rules: What’s Fair?

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  1. Voting Rules: What’s Fair? • Q. What is the most fair voting rule? Suppose three proposals to spend $15: • Z=Status Quo (currently, we spend $10 on guns and $5 on butter) • X= Proposal (peaceniks want to spend $5 on guns and $10 on butter) • Y=Amendment on Proposal (health nuts want to spend $10 on margarine) • And 11 voters with preferences as follows: • Voters 1 - 5 (5): X p Y p Z • Voters 6 - 9 (4): Y p Z p X • Voters 10-11 (2): Z p X p Y

  2. Method 1: Plurality Voting (1 person one vote, the choice with the most votes wins) • AlternativeVotes • X5 • Y4 • Z2 • Voters 1 - 5 (5 voters): X > Y > Z • Voters 6 - 9 (4 voters): Y > Z > X • Voters 10-11 (2 voters): Z > X > Y

  3. Method 2: Borda Count (each alternative receives “score” based on rank in each voter's ordering -- here, 2 points if most-preferred, 1 if second, none if third). • AlternativeFirst-placeSecond-place Total Votes Votes Points • X5212 • Y4513 • Z248 • Voters 1 - 5 (5 voters): X > Y > Z • Voters 6 - 9 (4 voters): Y > Z > X • Voters 10-11 (2 voters): Z > X > Y

  4. Method 3: Amendment Procedure (sequentially vote on pairs of alternatives) • Option 1: vote on type of change first, then on status quo versus change. Status quo wins. • X vs. Y (X wins, 7-4) X vs. Z (Z wins, 6-5) Z is ultimate choice • Option 2: vote on proposal first, then allow amendments to outcome. Amended proposal wins. • Z vs. X (Z wins, 6-5) Z vs. Y (Y wins, 9-2) Y is ultimate choice • Option 3: Vote on amendment first, then on final bill (whether proposal or amended proposal). Unamended proposal wins. • Z vs. Y (Y wins, 9-2) Y vs. X (X wins, 7-4) X is ultimate choice

  5. Strategic voting: • Option 2, amendment voting, but voters 10-11 vote for X even though they prefer Z. • Why: if X wins, it will beat Y on next vote, yielding a result these players prefer to result of sincere voting, Y. • Option 2 with sincere voting : • Z vs. X (Z wins, 6-5) • Z vs. Y (Y wins, 9-2), Y is ultimate choice • But with strategic voting: • Z vs. X (X wins, 7-4) • X vs. Y (X wins 7-4), X is ultimate choice

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