[EM] Thoughts on Burial

[Juho]

On Jul 25, 2010, at 4:51 PM, Jameson Quinn wrote:

>
>
> 2010/7/23 Kristofer Munsterhjelm <km-elmet at broadpark.no>
> Jameson Quinn wrote:
>
> I've been thinking recently about systems which enforce chiral  
> symmetry, making condorcet ties impossible. While it is possible to  
> "solve" the truncation/burial problem (eg, between two near-clones  
> who split a weak majority) in this way, I have not been able to come  
> up with an acceptably simple system. The closest I know of is  
> "tournament seeding"-style, condorcet-compliant (though not  
> necessarily condorcet-based) systems, where only certain pairwise  
> races are considered. In such systems, burial/truncation is a  
> nonstrategy, period.
>
> I think I read somewhere that elimination tournament methods must  
> fail monotonicity. I do know that runoff-type elimination based on  
> weighted positional methods (e.g. IRV being based on Plurality, and  
> Borda-elimination being based on Borda) must fail monotonicity.
>
> That seems wrong to me. A simple random seeding and binary-tree (as  
> in world cup elimination) pairwise tournament method is, as far as I  
> can see, monotone. However, if you base the seeding on random  
> ballot, then it probably does fail monotone.
>
> If parties are a factor, you could seed based on last-election  
> performance. For instance, make a matrix of average-number-of- 
> candidates-in-between, with tied candidates counting as half, and  
> seed one round at a time so that the closest candidates face each  
> other. New parties would be seeded randomly. This method would be  
> very easy to explain to any sports fan (even though my seeding,  
> unlike world cup seeding, would pair off near-clones - even two  
> strong near-clones - in the first round, so that mutual burial  
> between those two groups becomes counterproductive in later rounds).
>
> The problem is, while this method avoids the near-clone burial  
> problem (when the seeding works), it is vulnerable to a more-general  
> turkey-raising burial strategy, which could lead to DH3-type  
> pathology. Oh well.
>
> JQ
>

There can be many kind of seeding / predetermined ways to order the  
comparisons. Different cases offer different kind of strategic  
opportunities.
1) purely random
2) derived from the election results
3) given by candidates / parties (parties, trees)

Here's one way to arrange the candidates in category 2.

Start top down. Split the candidates in two categories. Out of all  
possible divisions pick the one that divides the candidates in most  
clone like groups. Then proceed down in the same way in both branches  
until the size of all the undivided subgroups is 1.

One could make the split as follows. (Ties will not be covered.)  
Candidates A, B, C, D, E, and F will be divided in two groups. One  
possible division is ABC - DEF. If A, B and C are clones and D, E and  
F are clones, then this division is perfect. If they are not, then  
count points that break this clone property. If someone voted  
A>D>B>C>E>F, then this fails being a clone vote. The strength of that  
failure is 1 since one can divide this vote e.g. as ADBC - EF and only  
one candidate does not follow the given clone division. In vote  
A>D>B>E>C>F one can make only divisions that violate the clone  
division in 2 places. Then one sums up all the (smallest) violations  
in all votes (for all possible divisions). The division with lowest  
score is the best division.

Category 2 methods are not be fully strategy free but maybe the  
strategies are at least more difficult to apply due to the increased  
complexity :-).

Juho






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