[EM] Top Two Runoff versus Instant Top To Runoff

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:
> 
>  
> Kevin,
>  
> I know that you have studied Top Two Runoff more deeply than I have. 
>  
> Here in Oregon measure 65 was defeated recently.  It was a version of 
> top two runoff in which the the first round of the runoff replaced the 
> traditional primaries, i.e. it was cast as one grand open primary for 
> all parties and all voters, from which the top two vote getters advance 
> to the other stage in November.
>  
> It was interesting that the IRV organization FairVote was against the 
> measure, even though there was no IRV initiative on the ballot.
>  
> It seems to me that Top Two Runoff might be more manipulable than the 
> instant version of the same, since voters could vote insincerely in the 
> first round without having to worry about that messing up their choice 
> in the other stage.
>  
> I would be interested in your thoughts on this matter.

I'm not Kevin, but I think I can comment. In any method that's [some 
base method] + runoff, where the runoff candidates are picked from the 
social ordering of the base method, the existence of the second round 
would increase the incentive to strategize.

However, it would not make it safe to always strategize. Say that the 
runoff method is "pick first and second place winners of the base 
method". Then any strategy that boosts your preferred candidate to 
either first or second place can be used - but if the strategy, when 
applied too greedily, causes both first and second place to be replaced 
by candidates you don't like, there's an incentive to be careful.

That's weaker than it is for just applying the base method and picking 
the winner. If you use strategy in the base method case, and you 
displace your true winner in favor of someone that you really loathe, 
then you're out of luck. For that to deter you from using strategy in a 
runoff, it has to displace both the candidates that would get into the 
runoffs.

One should also be aware that the second round, taken as a separate 
election, will be honest. That's because there are only two candidates 
and a simple majority election is strategyproof in that case. So that 
may weight against the increased incentive to use strategy in the first 
round. Whether this makes the method (in general) more fragile 
(attracting more strategy) or more robust depends on which component is 
stronger: the incentive to strategy in the first round, or to honesty in 
the second. That probably depends on the base method.

There may also be inter-round strategy. Say that there are two wings and 
a center. In the first round, the left wing runs a strategy. It's 
discovered. Now, the centrists may support the right-wing candidate in 
the second round "just to show them", whereas they wouldn't otherwise. 
To the degree that runoffs are two elections, such effects may occur.