[EM] Proportional Lottery Application

[Forest Simmons]

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
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