[EM] Generalized symmetric ballot completion

[Juho Laatu]

On 31.5.2011, at 12.58, Peter Zbornik wrote:

> That would be, I think the smallest improvement on IRV, which could make a positive change in real life and would support centrist candidates.

From the Condorcet criterion point of view, the Condorcet winner is a good, often "centrist" candidate. If Condorcet criterion is one of the targets to be met, then IRV could be modified appropriately. One simple trick that has been proposed is to eliminate the pairwise loser of the two candidates with least votes (instead of eliminating always the candidate that has least votes).

(If IRV is used to pick candidates for a second round, and if centrists are interesting, then maybe Condorcet winners should be kept.)

> - Using explicit cutoff just as an extra candidate that voters can use as a strategic tool to generate big defeats to some candidates is more problematic (you can try to bury someone under X without any risk of electing X)
> You can try to bury someone under all other candidates anyway. Introducing a null-candidate as a "cuttoff" does not change that.

Yes, but in traditional burial there is always a risk that when voters "lie" that candidate Z is better than it is (in order to bury someone) that introduces also a risk of electing Z, and that is one key factor that makes burial strategy usually too dangerous to try. If there is a "candidate" that can be used for burying but that can not be elected, burying may become less risky and therefore more common.

> My approach to the various criteria is that one should take into account also how much some method violates some criterion. No proper method meets them all. Condorcet methods are very good from this point of view in the sense that although they fail Later-no-harm there is "usually and by default" no harm ranking also "later" candidates. Same with burial. They are vulnerable to burial but "usually and by default" one need not worry about burial (=not a practical strategy in typical large public elections with independent voters).
>  
> OK for public elections, but for a political party, where voting strategy is the name of the game?

The risk of rational strategies increases if the election is competitive (all political elections tend to be), the number of voters is small, their voting behaviour can be reliably and centrally coordinated (e.g. direct commands from one's own party), information on the planned strategy does not leak out to others, when the preferences of all voters are already known (maybe there already was a test vote), and when other groups are probably not going to use any strategies. If there are multiple parties that may apply strategies and counter strategies things come more complicated again. Things may become more complex also if some groups try to fool others or hide information by giving false messages and false data in polls (maybe in a coordinated way) before the actual election. In small elections strategies may thus become easier, but still, it is hard to generate any easy rules that could be followed by a strategic grouping to implement rational and successful strategies in Condorcet methods. My understanding thus is, "good for almost any competitive elections".

Actually I have asked on this list couple of times for good strategy advices for practical elections (i.e. 100% accurate information of the given votes + option of exactly one grouping to change their voting behaviour after the election will not do (this is how the vulnerabilities are typically described on this list and elsewhere)) but I have not seen any yet. (I have my own favourites for the weakest spots, none of them not terribly weak, but I'd like others to step out and tell how Condorcet methods can be fooled best when the available information is just few inaccurate and contradictory polls, and the opinions are likely to still change a bit before the election day.)

> Do you have any references for your statements concerning "usually and by defaults"?

That was just my way of saying that vulnerabilities exist but they tend to be marginal.

> If there is a top level cycle, then people may afterwards think "I should have voted that way", but it is not easy to know what to do (except to vote sincerely) before the election.
>  
> I don't aggree. There is polling and the voter normally knows who is the biggest competitor to the "favored" candidate. The competitor is buried. The voters for the competitor bury your favorite candidate, and the winner is a "nobody" that no-one cared enough about to out-maneuver and noone supports, but also noone dislike. In a polarized environment that is not an unlikely scenario.

Are you saying that general burying of one's competitors is a rational strategy for all voters? I.e. is that strategy likely to bring more benefits than problems? I believe that in most cases burial is harmful to the strategist.

> I do not personally like the idea of keeping the voter "uninformed" of the workings of an election system and their different strategies.
> That is a path I do not want to walk.

Me neither.

Juho




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