Voting Rules: What

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Voting Rules Whats Fair?

• Q. What is the most fair voting rule? Suppose
  three proposals to spend 15
• ZStatus Quo (currently, we spend 10 on guns and
  5 on butter)
• X Proposal (peaceniks want to spend 5 on guns
  and 10 on butter)
• YAmendment 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

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Method 1 Plurality Voting (1 person one vote,
the choice with the most votes wins) Alternat
ive Votes X 5 Y 4 Z 2 Voters
1 - 5 (5 voters) X gt Y gt Z Voters 6 - 9 (4
voters) Y gt Z gt X Voters 10-11 (2 voters) Z
gt X gt Y
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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). Alternative First-place Second-pla
ce Total Votes Votes Points X 5 2 12 Y
4 5 13 Z 2 4 8 Voters 1 - 5 (5
voters) X gt Y gt Z Voters 6 - 9 (4 voters) Y
gt Z gt X Voters 10-11 (2 voters) Z gt X gt Y
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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
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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