# [EM] Yet Another Lottery Method

Jobst Heitzig heitzig-j at web.de
Sun Jun 25 08:24:50 PDT 2006

```Dear Forest!

Very nice idea indeed. It goes somewhat in the same direction I am also thinking recently. I will think about it during the next days.

What I'm studying at the moment is how Random Ballot can be modified so that cooperation is encouraged.

For example: Use approval ballots, find out which X is approved most often, mark X on all ballots that approve her, put these ballots aside, then find out which Y is approved most often on the remaining ballots, mark Y on these ballots and put them aside, proceed likewise with the remaining ballots until all ballots are put aside, then draw one ballot at random and elect the marked candidate.

In addition to such a cooperation-encouraging version of Random Ballot, one should use some mechanism to protect from dangerous candidates, such as your approval-defeats, or just by allowing voters to indicate "dangerousness" of candidates and excluding all candidates who got more than, say, 75% such dangerousness-marks.

Yours, Jobst

> -----Ursprüngliche Nachricht-----
> Von: "Simmons, Forest"
> Gesendet: 24.06.06 01:22:59
> An:
> Betreff: [EM] Yet Another Lottery Method

> This method makes use of ordinal information as well as approval information.
>
> 1. Eliminate each candidate X for which there is a candidate Y such that on each of more than half of the ballots Y is approved and X is not.
>
> 2. Use random ballot among the remaining candidates to choose the winner.
>
> Note that if any candidate X is eliminated, then some candidate Y must have more than fifty percent approval, which makes her invulnerable to elimination.
>
> This method satisfies Monotonicity, Clone Independence, Independence from Pareto Dominated Alternatives, Strong Favorite Betrayal Criterion, etc. In fact, as near as I can tell there is no incentive for any insincere order reversal or collapse.
>
> Of course, Random Ballot without step 1 satisfies all of those criteria, too, but it is a bit too promiscuous with the probability.
>
> With this new method any united majority can eliminate any dangerous candidate from consideration. This majority defense feature has a name, but I won't try to remember what it is.
>
> Forest

> -----Ursprüngliche Nachricht-----
> Von: "Simmons, Forest" <simmonfo at up.edu>
> Gesendet: 25.06.06 02:33:23
> An: <election-methods at electorama.com>
> Betreff: Re: [EM] Yet Another Lottery Method

> Ralph suggested that in the example
>
> 45 B>A>>C
> 40 C>>A>B
> 15 A>C>B
>
> the smallest faction might prefer a 100% C lottery to a 55%A+45%B, and in that case approving only C would be better than approving only A.
>
> But if  100%C is better than 55%A+45%B, for the A>B>C faction, then  60%A+40%C would be better still for that faction.  So their best bet is to vote sincerely  A>C>>B .
>
> Forest
>
>
> Ralph's example & commentary:
>
>
> 45:  A, B approved  ( B>A>>C )
> 40:  C approved ( C>>A>B )
>
> The remaining 15 voters are of the opinion
> A>C>B
>
> if they approve A only:
> C is eliminated ( 45+15 = 60 votes approve A and not C )
>
> result is:
> A: 40+15 = 55%
> B: 45 = 45%
> C: elim = 0%
>
> OTOH, if they approve C (tactical voting)
> A,B are eliminated ( 55% approve C and none other)
>
> results is
> A: elim= 0%
> B: elim= 0%
> C: 100% ( only remaining )
>
> It is not clear to me that a 55% chance of your favorite and 45% chance
> of your lowest choice is superior to a 100% chance of your middle
> choice.
>
> This means that depending on the 15 voters relative preference
> strengths,
> it might be in their interests to tactical vote and just approve C,
> even though
> they prefer A to C.
>
> If the ranked choice must be consistant with the approval choice, they
> could
> just vote C approved and C first choice as a pure tactical vote.
>
>
>
> <hr>
> ----
> election-methods mailing list - see http://electorama.com/em for list info
>

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