[EM] Clone-proof STAR (Score+Automatic Runoff)

[Kristofer Munsterhjelm]

On 07/25/2017 08:46 PM, Ted Stern wrote:
> [Related to a topic that was discussed earlier on the Election-Methods
> list --
> http://election-methods.electorama.narkive.com/Vlwq75Zy/em-top-two-approval-pairwise-runoff-ttapr
> ]
>
> STAR is described here: http://www.equal.vote/
>
> It is vulnerable to crowding -- too many clones could prevent the
> top-two score winners from capturing the variance-minimizing candidate
> in the pairwise runoff.
>
> One relatively simple way to deal with clones is to reweight the ballots
> of voters, and then choose one of the remaining candidates in some way.

Some DSV thoughts along those lines:

The most obvious way of making crowding go away is to simply remove the 
ballots of the voters who voted for the winner. But that may cause 
regret because of a vote-management situation, e.g. X has total rating 
100, Z has total rating 91, and Y has total rating 90; and someone who 
voted for both X and Y gets his vote removed, whereas he could have 
helped Y get more votes if he hadn't voted for X. So he would have 
preferred to only vote for Y unless that would have made X lose.

So suppose X is the Range winner and so is chosen as one of the top two. 
Then we could do a (relatively simple) DSV this way:

For each other candidate Y, maximize Y's score by turning "X and Y" 
votes into "only Y" votes, subject to:
- X has to be the Range winner (i.e. top scoring candidate) after the 
transformation too - or Y has to be the Range winner and X second,
- You have to remove all remaining untransformed "X and Y" votes when 
counting Y's support.

The transformation would only be temporary, i.e. when considering Y's 
score, use the unmodified ballots + transformation to get Y's score, 
then when considering Z's score, use the unmodified ballots + 
transformation to get Z's score. The candidate with the greatest 
modified score is the second candidate for the runoff.

Unfortunately, this is rather complex, and simplicity is supposed to be 
STAR's thing, so I don't know how useful it is. There may be some second 
order/pushover strategy incentive as well, e.g. someone who wants Z to 
win, where Z is not very well liked by X-voters and Y is in second place 
by unmodified ratings, votes Z and Y so as to decrease the margin X has 
down to Y, in an attempt to deny "X and Other" votes from going to Other.

(Using this kind of DSV is much easier with threshold-based methods 
because then the threshold is fixed, so the second order strategy is 
rendered moot.)