[EM] truncation dilemma

[Juho]

The ordering need not be random. One can use also a tree structure as  
given by the candidates. Clones and near clones will form branches.  
The simplest approach is to consider defeats within a branch to be  
weaker than defeats between branches.

Juho



On Jun 26, 2010, at 4:01 AM, Jameson Quinn wrote:

>
>
> 2010/6/25 <fsimmons at pcc.edu>
> >1a. Probabilistic dilemma. If truncation causes a cycle, then there  
> is some
> probabilistic tiebreaker which always includes some chance of C  
> winning.
> This can act as a goad to A and B voters to cooperate. I suspect  
> that some
> system like this might be the theoretical optimum response if voters  
> were
> pure rational agents; however, real people tend not to like  
> probabilistic
> election systems.
>
> Sports fans don't object to the use of a certain amount of  
> randomization in deciding the order of contests
> in a tournament.
>
> True, and good point.
>
> Still, sports aren't elections. Sports are intended to be exciting,  
> and so an element of chance can be a positive advantage. Also, since  
> only a limited number of sequential two-way contests are possible,  
> there is really no alternative to a seed order, unlike with election  
> systems which have (too) many alternatives.
>
>
> A single elimination tournament, for example, needs a "seed" order.   
> If a random order is not used, then
> (if I remember correctly) the contestants with the better records  
> are seeded near the end of the
> tournament, to avoid anticlimatic contests at the end of the  
> tournament.
>
> I suggest the following way of picking a seed order SO for an  
> election:  use the order of a random ballot
> refined by the orders of additional ballots until the order is  
> complete.
>
> One way to use the seed order SO is by single elimination, starting  
> at the bottom of the list and working
> up.
>
> Another (distinct!) way is to elect the lowest alternative on the  
> list that pairwise beats every alternative
> listed above it.
>
> Here's my favorite: initialize X as the highest alternative in the  
> SO.  While X is covered, replace X with the
> highest alternative on the SO that covers X.  Then elect the final  
> value of X.
>
> When the seed order SO is the refined random ballot order as given  
> above or any other social order that
> is monotone and clone free, these methods will pick from the Smith  
> set, while preserving the clone
> independence and monotonicity.  Furthermore, the last of these (my  
> favorite), satisfies Independence
> from both Smith and Pareto Dominated Alternatives, and will elect  
> from the uncovered set.
>
> Do these methods solve the truncation dilemma?
>
> Mostly. With a given seed ordering, if you are a B>A>C voter, a  
> B>A=C vote cannot change the winner from A to B, unless it causes C  
> to cover B. This is only possible if, with honest ballots, C beats B  
> and B beats A. Neither of these are consistent with a truncation  
> dilemma scenario.
>
> There's still a possibility that your ballot is one of the random  
> ballots that helps define the seed, and so your strategic vote  
> causes C to come first in the seed order, AND causes A not to cover  
> C, so that B is then elected. So, your "refined by additional random  
> ballots until the order is complete" could break the truncation  
> resistance. I suspect - but am not sure - that a "single random  
> ballot refined by random choices" seed order would not have a  
> truncation-dilemma.
>
> ... On a separate note, perhaps the "covering" concept is too hard  
> to explain. How much better is that than simply a single bubble sort  
> pass up from the bottom of the seed order? That would also guarantee  
> Smith set.
>
> JQ
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> Election-Methods mailing list - see http://electorama.com/em for  
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