[EM] Proportional Lottery Application

[Forest Simmons]

We want a defeat strength of 100 percent for A>B when the pairwise winner A
is the CW and the pairwise loser B is the CL. So ...
Sum f(X) such that X does not defeat A
Minus
Sum f(Y) such that B defeats Y

Did I finally defeat my senior moment?

(More like senior week:-))

-Forest

On Sun, Oct 23, 2022, 2:37 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> If my intuition is correct, then the appropriate "first place margins"
> defeat strength for A>B would be the following difference of sums ...
>
> Sum f(X) over X not defeated by B
> Minus
> Sum f(Y) over Y defeating A
>
> Does that make sense?
>
> -Forest
>
>
>
> On Sun, Oct 23, 2022, 1:46 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> 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.
>>>
>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20221023/d66fe126/attachment.htm>