[EM] The Green scenario, and IRV in the Green scenario, is a new topic here. Hence these additional comments. Clarification of position and why.

[Kristofer Munsterhjelm]

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?