[EM] A Proportionally Fair Consensus Lottery for which Sincere Range Ballots are Optimal

[Jobst Heitzig]

Folks,

you probably overlooked that I have already described a variant which
works *completely* without Random Ballot and will definitely elect one
of the top-3 range options (as determined from the 'strategic' ballot):

> Method "Range top-3 runoff" (RT3R)
> ===================================
> 
> 1. Each voter separately supplies
>    a "nomination" range ballot and a "runoff" range ballot.
> 
> 2. From all "nomination" ballots, determine
>    the options A,B,C with the top-3 total scores a>b>c.
> 
> 3. Let L be the lottery in which B wins with probability
>    p = max(0,(2b-a-c)/(b-c))  and C wins with probability 1-p.
> 
> 4. Let q be the proportion of "nomination" ballots
>    on which the lottery L has an expected rating
>    below the rating of A on that ballot.
> 
> 5. Option A wins if,
>    on at least the same proportion q of all "runoff" (!) ballots,
>    the lottery L has an expected rating
>    below the rating of A on that ballot.
>    Otherwise B wins with probability p and C wins with probability 1-p.
> 

So if you want it to be as deterministic as possible, you can do it like
this or similarly. If you modify it further and set q=1/2, you even get
a majoritarian version if you want that.

Yours, Jobst



Warren Smith schrieb:
> --yep.  Only reason I did what I did was simplicity (kind of a pain if
> voters have to submit
> both a range-type and a condorcet or approval-type ballot).
> But your way is better in that it tends to yield a better winner than my way.
> 
> Also, note -- which is even more obnoxious -- we could have each voter
> submit TWO ratings-style ballots,
> the "honest range ballot" and the "dishonest range ballot"; then the
> HRB is used to
> decide between DHR and random ballot...
> 
> 
> On 11/20/09, Raph Frank <raphfrk at gmail.com> wrote:
>> This is effectively performing random ballot and then giving the
>> voters the option to roll the dice a second time.
>>
>> Any single seat method could be used to select the first candidate.
>> If you used a good single seat method to pick the compromise winner,
>> then the random ballot would rarely if ever be activated.
>>
>> For example.
>>
>> 1) Voters submit ratings ballot and also a ranked or an approval ballot
>> 2) Determine the winner using condorcet or approval (or other method)
>> 3) Determine the random ballot odds for each candidate
>> 4) If a majority prefer the winner in 2 to the expectation in 3), then
>> the winner from 2 wins.
>> 5) Otherwise, use the random method
>>
>> Ofc, using a majority instead of a unanimous decision breaks some of
>> the properties of the pure consensus method.
>>
> 
>