[EM] another concern - the opposite of the Spoiler Effect - *Packing*

[Kristofer Munsterhjelm]

On 06/28/2013 03:30 AM, Benjamin Grant wrote:
> Something else came up while I was analyzing some voting methods.  If
> you have a disproportionate number of political leaning in an election,
> some voting systems go awry.
>
> There may be a criterion for this, this is what I mean.
>
> Let’s say that you have three total candidates.  one is conservative,
> two are liberal, none are moderate.  If the majority of the electorate
> is conservative, then it may make sense that a conservative gets
> chosen.  However, in some systems – say one in which each voter gets one
> positive vote and one negative vote to cast – having more candidates of
> a particular “wing” can hurt you. Continuing this example, if we run
> Gore/Nader/Bush, both Gore and Nader supporters give their negative
> votes to Bush, casting their positive votes for their own candidate.

This is what clone independence is supposed to check. Usually clone 
independence is considered as one criterion, but when it's subdivided, 
it's usually into three:

- Vote-splitting, where cloning a winner makes him lose,
- Teaming, where cloning a loser makes him win,
- Crowding, where cloning a loser makes some other loser win,

with examples:

- Vote-splitting: cloning A changes the win from A to B,
- Teaming: cloning A changes the win from B to A,
- Crowding: cloning A changes the win from B to C.

Vote-splitting is the standard Plurality problem. It seems what you're 
talking about is teaming, which is the opposite of vote-splitting (in a 
sense). Crowding is more of a "chaos happens" thing.

The Wikipedia article on the clone independence criterion calls teaming 
"clone positive" and vote-splitting "clone negative". See 
https://en.wikipedia.org/wiki/Independence_of_clones_criterion .

> Is this a thing? Kind of the opposite of the spoiler effect – that
> having many like-minded candidates actually increases the chance that
> one of them might win, even if their opposition is more numerous?
>
> Does this only happen with negative votes?  Or can it happen with other
> methods?

The typical method where teaming works is Borda. In Borda you have n 
candidates and the first ranked gets (n-1) points, the next (n-2) points 
and so on down. No voter gets a negative score.

More generally, consider a weighted positional system where the first 
rank gets x_1 points, second rank x_2 points and so on. This system is 
equivalent to one where the first rank gets x_1 + Q points, the second 
rank gets x_2 + Q points and so on, for any constant Q. So it can't only 
happen with negative votes, because you could make Q large enough so 
that all the weights were positive, and it would be the same method.

Though that's probably not what you meant. Teaming can happen with 
methods that aren't weighted positional as well. On the Wikipedia 
example, there's an example of teaming happening in Copeland (the 
"sports tournament" method). More obviously, a method that just picks a 
random candidate as the winner exhibits teaming, because the more 
candidates you can add of your own stripe, the more likely the 
figurative roulette wheel is to stop at one of your own candidates.