On 02/04/2013 09:31 PM, Peter Zbornik wrote:
Hi I am afraid a proportional approach in the first round wouldnt
work, it opens up for strategic voting.
Say we have an election with A, B, C.
45 A
30 B A
25 C B A
The first round in a 2-seat election the quota is 34 votes
If we would have a two-round proportional election, then B would win
in the second round.
So A's voters find this out and decide to change their preferences and
10 of the voters of A vote for C
So we have
35 A
30 BA
25 CBA
10 CA
C and A meet in the second round, where A wins.
A one-on-one runoff (i.e. second round), taken on its own, is
strategy-proof. However, if we imagine the voters never change their
opinion, then we could build a ranked election system that works as
however the first round would in reality, then simulates a runoff
between the winners. This method would, like any other ranked method, be
subject to Arrow's theorem and to Gibbard-Satterthwaite.
Thus, the runoff can't, as a whole (both rounds considered) be
strategy-proof. So there will be some kind of strategy. But does a
proportional first round make it more vulnerable to strategy than a
plain first round?
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