[EM] Sequential-Pairwise offensive & defensive strategy?

[Forest Simmons]

On Wed, Sep 20, 2023, 10:31 PM Michael Ossipoff <email9648742 at gmail.com>
wrote:

> Yes, that fancier Sequential Pairwise ordering method would make it harder
> for a strategist to guess anything about the comparison-order…when, instead
> of the candidate’s top-count, it uses the sum of the top-counts of those
> above him on each ballot.
>

By the way this top weighted Borda count is just as efficiently precinct
summable as Borda itself: to get respective scores of the candidates
multiply the pairwise support matrix on the left by the row vector of top
respective counts ... which can be conveniently stored as diagonal elements
of the pairwise support matrix whose off diagonal element in the j_th row
of the k_th column is the number of ballots on which candidate j outranks
candidate k.

This summability is a big advantage. There were lots of complaints about
the slowness of RCV vote transfers between elimination rounds.

>
> An extra layer of unpredictability for a would-be strategist.
>
> The vulnerability of the simplest-defined procedure would have to be
> weighed against what polls & focus-groups say about people’s requirement
> for definition-simplicity & brevity.
>
> Undeniably the more multi-layered & unpredictable ordering procedure is
> more strategy-proof & better.
>
> Strategy-evaluation for Condorcet-complying pairwise-count methods has
> proven to be complicated & more difficult than one would expect.
>
> But it now seems for sure that there are such methods that are
> sufficiently offensive-strategy-proof or well-protected from
> offensive-strategy.  It’s only a question of how many & which ones.
>
> The Condorcet-IRV-Runoff hybrids hold promise, with merit to always be
> balanced with what is heard in polls & focus groups about
> definition-brevity.
>

One piece of redundancy I recommend in any Condorcet efficient method
definition ... start with words to the effect "If there is no majority Top
candidate, elect the candidate that is undefeated in every head to head
matchup. And in the extremely rare case that no such ideal candidate
exists, elect the candidate closest to this democratic ideal as follows:

>
> So I’m sure that I’ll propose & recommend good Condorcet versions (even if
> I don’t yet know which ones & how many) over IRV.
>
> …but I’ll nonetheless include IRV among the methods that I offer, because
> it’s better than a lot of people believe.   …though its merit & workability
> strongly depend on the electorate & the candidate-lineup.
>
> I.e. Because it isn’t Condorcet-complying, it’s necessary that the
> electorate aren’t timid lesser-evil giveaway voters.
>
> But an electorate that has just enacted IRV in a referendum didn’t do so
> because they want to rank Lesser-Evil over their favorite. They enacted it
> because they want to rank sincerely, to express & fully help their favorite.
>
> Let’s support Oregon’s IRV (RCV) referendum next year!
>
> Though IRV doesn’t meet the Condorcet Criterion, it meets Mutual-Majority:
>
> IRV always elects the candidate of the largest faction of the
> Mutual-Majority.  …The favorite candidate of the Mutual-Majority.
>
> IRV didn’t “fail” in Burlington & Alaska. It did what it’s supposed to do.
>
> We don’t yet have a big Condorcet organization, or referenda, initiatives
> or strong lobbying for it, but let’s support the already ongoing enactment
> efforts for IRV, now named RCV.
>
>
> On Wed, Sep 20, 2023 at 18:24 Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> So called BTR-IRV, "Bottom Two Runoff IRV" goes along those lines.
>>
>> You probably remember "Benham" that runs IRV elimination until there
>> remains a candidate undefeated by any of the other remaining candidates.
>>
>> This reminds me of basing the Sequential Pairwise Elimination agenda
>> order on Top preferences ... by using those preferences to "de-clone" the
>> Borda agenda order:
>>
>> The agenda order is given by SB(X), the Sum over all ballots B of the
>> first place votes of the candidates ranked above X on B.
>>
>> The larger SB(X), the later X is (on average) in the rankings, and the
>> rearlier X is in the elimination agenda.
>>
>>
>>
>> On Wed, Sep 20, 2023, 4:56 AM Michael Ossipoff <email9648742 at gmail.com>
>> wrote:
>>
>>> If, using voted rankings, Sequential-Pairwise’s comparison-order is
>>> determined by giving, to the candidates with higher top-count score, a
>>> later position in the comparison-order, so that voters don’t know what the
>>> comparison-order will be…
>>>
>>> …
>>>
>>> …& if voters’ knowledge of eachother’s preferences is no better than it
>>> is now in political-elections…
>>>
>>> …
>>>
>>> …Does that Sequential-Pairwise election have an offensive strategy with
>>> gain-expectation comparable to what it would have in MinMax, RP & CSSD?
>>>
>>>
>>>
>>> …And, if so, is there a defensive strategy to thwart or deter that
>>> offensive strategy?
>>>
>>>
>>>
>>> …That seems of interest because Sequential-Pairwise is so much less
>>> computationally-demanding than the other pairwise-count methods.
>>>
>>> If, using voted rankings, Sequential-Pairwise’s comparison-order is
>>> determined by giving, to the candidates with higher top-count score, a
>>> later position in the comparison-order, so that voters don’t know what the
>>> comparison-order will be…
>>>
>>> …
>>>
>>> …& if voters’ knowledge of eachother’s preferences is no better than it
>>> is now in political-elections…
>>>
>>> …
>>>
>>> …Does that Sequential-Pairwise election have an offensive strategy with
>>> gain-expectation comparable to what it would have in MinMax, RP & CSSD?
>>>
>>>
>>>
>>> …And, if so, is there a defensive strategy to thwart or deter that
>>> offensive strategy?
>>>
>>>
>>>
>>> …That seems of interest because Sequential-Pairwise is so much less
>>> computationally-demanding than the other pairwise-count methods.
>>>
>> ----
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>>>
>>
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