[EM] Proportional Lottery Application

[Forest Simmons]

Thanks, Jobst. I worked carefully through the Random Ballot Favorite Chain
Building lottery example, but in the leap from RBFCB to the Ranked Pairs
interpretation I carelessly forgot to accommodate clones.

Here's what I think it should be:

The defeat strength for the pairwise defeat A>B should be the sum of f(X)
over all X that are not defeated by B ... not just fA).

So if A is the CW, the defeat strength of A>B would be 100 percent, no
matter the candidate B or the clone B' of B.

Does that seem right?

Also, if A is not the CW, and A' covers B, then the defeat strength of A>B,
would be no greater than the defeat strength fo A'>B.

So it seems to be the defeat strength we want, whether or not our leap from
the RBFCB lottery to Ranked Pairs was justified logically.

After Kevin and Kristofer test it experimentally we'll know it it's any
good. The proof is in the pudding!

-Forest

On Sun, Oct 23, 2022, 12:11 AM Jobst Heitzig <heitzig at pik-potsdam.de> wrote:

> Hi all, just shortly due to lack of time: When you say "benchmark lottery"
> you mean random ballot, right? But then we measure defeat strength by
> number of first-place votes, right? So how do we achieve clone-independence
> then? Shouldn't we measure defeat strength by approval score instead to
> make it clone-independent? Or is some decloning involved to construct your
> notion of benchmark lottery that I missed? All the best, Jobst
>
> Am 23. Oktober 2022 00:36:41 MESZ schrieb Forest Simmons <
> forest.simmons21 at gmail.com>:
>>
>> A nice convergence of ideas has brought us to a practical proposal.
>>
>> The first idea is Jobst's Proportioal Lottery (democratic fairness)
>> notion. If 30 percent of the voters bullet vote for X, then a fair lottery
>> ought to select X at least 30 percent of the time.
>>
>> The second idea, also due to Jobst, is that pairwise defeat strength
>> doesn't have to be overtly pairwise. Jobst was first to point out that DMC
>> can be construed as Condorcet with winning approval as the gauge of defeat
>> strength.
>>
>> The third idea introduced to the EM list by Jobst was Rivest's Condorcet
>> Lottery ... a non-proprtional, but Dutta efficient, lottery lacking only in
>> Monotonicity short of an ideal Condorcet method.
>>
>> The  fourth idea, also Jobst's, was Chain Climbing as a Banks efficient
>> selection procedure.
>>
>> The fifth idea central to the evolution of our practical proposal was the
>> importance of first place votes for de-incentivizing burial and Chicken
>> strategy, while simultaneously conferring Landau efficiency ... the result
>> of doggedly pursuing the Holy Grail of fpA-fpC when everybody else
>> despaired.
>>
>> Kristofer's important "Friendly" classification of candidates arose in
>> that context.
>>
>> Kristofer, Kevin, and Chris Benham (among many others) also continued
>> championing the kernel of good worth emulating in IRV ...  hence Benham's
>> method as the original genesis of DMC, and our widespread use of first
>> place counts for emulating IRV's clone independence, and avoiding burial,
>> Chicken dilemma, etc.
>>
>> The idea of Kristofer, Benham, Bristow-Johnson, and many others that we
>> should keep the strategic burden off the backs of the voters by striving to
>> bring into the Universal Domain the successes first achieved outside that
>> domain ... the ones that benefitted greatly from the help of Approval
>> cutoffs, Voting Published Rankings, candidate asset/proxy options, etc.
>>
>> For a long time the only monotone, clone independent, Landau efficient
>> methods we could devise (like score based chain climbing) depended on
>> approval or other (non-UD) score orders. Eventually, [with the advent of a
>> de-cloned Kemeny-Young version we called Swap Cost] we got a clonefree,
>> monotone, UD finish order that we could chain climb to get a Banks
>> efficient method entirely within the UD domain.
>>
>> De-cloning Kendall-tau in order to de-clone K-Y) relied heavily on the
>> benchmark lottery probabilities, as well as on the anti-favorite lottery
>> probabilities.
>>
>> [The cost of swapping (reversing) an adjacent pair order in a permutation
>> of the candidates ... is the product f(D)f'(A) where f is the first place
>> probability of the descending candidate D, and f'(A) is the anti-benchmark
>> lottery probability of the ascending candidate A; the cost of lowering a
>> candidate is proportional to its percentage of the top votes, while the
>> cost of raising it is proportional to its percentage of the bottom votes.]
>>
>> Finally, as Jobst pointed out recently, the prominent rôle of first place
>> votes in Friendly Voting helps prevent weak centrists, from taking undue
>> advantage of Condorcet's reliance on relative, as opposed to absolute
>> preferences.
>>
>> Which brings us, without further ado, to our basic proposal:
>>
>> Condorcet (first place vote strength).
>>
>> That's it ... Condorcet, whether RP, CSSD, or River (it makes no
>> difference) ... with defeat strength gauged by the defeater's benchmark
>> lottery probability.
>>
>> That's all there is to it!
>>
>> At risk of detracting from the simplicity of the proposal, I cannot
>> resist the temptation to point out some advantages that the average voter
>> would not have any interest in, but are of great interest to every voting
>> methods connoisseur:
>>
>> 1. Without trying to be, this method turns out to be Landau efficient; no
>> covered candidate can win! This sets a new standard of immunity... there is
>> no good excuse any more for electing covered candidates ...  immunity
>> against various complaints must now include this one ... "But our candidate
>> not only defeated the alleged winner (head-head), she also defeated every
>> candidate the winner defeated ...  andno candidate that defeated the winner
>> defeated our candidate. So how do you explain that?"
>>
>> 2. The method, like IRV, is Chicken proof, burial proof, bullet proof,
>> etc.
>>
>> 3. The method is decisive; ties are as rare as first place ties under FPP
>> Plurality. Natural tie breakers for defeat strength can simply substitute
>> some other proportional lottery for the benchmark lottery.
>>
>> Since tie breaking is an important detail of every election law, humor me
>> to elaborate on this detail. The benchmark lottery probability that we are
>> using to gauge defeat strength for candidate X, is simply the percentage of
>> the ballots on which X is ranked highest. Here's a related proportional
>> lottery that could be used as a tie breaker: From a randomly drawn ballot
>> B, elect the highest ranked [tied] candidate that has a beatpath to every
>> other candidate ranked on B.
>>
>> Enough said for now!
>>
>> -Forest
>>
>
> --
> Diese Nachricht wurde von meinem Android-Gerät mit K-9 Mail gesendet.
>
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