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Technical discussion of election methods

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MinMax(wv), Schulze & RP(wv) (MAM) have some autodeterence.

MO
Michael Ossipoff
Wed, Feb 7, 2024 5:43 AM

For reasons I’ve mentioned, the CW is the most likely Topcount winner. The
CW faction is the most likely to be the largest.

Sincere rankings of the 3 factions:

CW, or CW>BF, or CW>Bus
Bus> CW
BF> CW

3 burial scenarios, each with the 3 factions’ rankings:

CW
Bus>CW
BF>Bus (burying)

CW>BF
Bus>CW
BF>Bus

CW>Bus
Bus>CW
BF>Bus

The BF & Bus factions, in the example  are equal in size. The CW faction is
larger. In an actual election, it isn’t known which of {Bus, BF} is bigger
than the other, & both possibilities are equiprobable.

In #1, Bus wins because the listed-methods meet Minimal-Defense.  …but you
can verify it, just as you can verify the results in the other 2 scenarios.

Scenario #2:

CW’s larger size gives factions give BF & bus the equally largest wv
against them. The largest wv against CW is less. CW wins.

Scenario #3:

CW’s larger size gives BF two instances of the largest defeat.

CW has an ordinary wv in its defeat, via the 2 smaller factions.

Because CW & Bus factions both rank Bus over BF, & only the BF faction
ranks BF over Bus, Bus pairbeats BF, with the maximal wv.

Bus wins by pairbeating CW & BF.

If CW is the largest faction (it’s the most likely to be the largest) &
nothing else about the burial-result is known, then BF, by the most likely
assumption, loses in all 3 scenarios, while Bus wins in the 3rd scenario.

The method has autodeterence.

For reasons I’ve mentioned, the CW is the most likely Topcount winner. The CW faction is the most likely to be the largest. Sincere rankings of the 3 factions: CW, or CW>BF, or CW>Bus Bus> CW BF> CW 3 burial scenarios, each with the 3 factions’ rankings: 1. CW Bus>CW BF>Bus (burying) 2. CW>BF Bus>CW BF>Bus 3. CW>Bus Bus>CW BF>Bus The BF & Bus factions, in the example are equal in size. The CW faction is larger. In an actual election, it isn’t known which of {Bus, BF} is bigger than the other, & both possibilities are equiprobable. In #1, Bus wins because the listed-methods meet Minimal-Defense. …but you can verify it, just as you can verify the results in the other 2 scenarios. Scenario #2: CW’s larger size gives factions give BF & bus the equally largest wv against them. The largest wv against CW is less. CW wins. Scenario #3: CW’s larger size gives BF two instances of the largest defeat. CW has an ordinary wv in its defeat, via the 2 smaller factions. Because CW & Bus factions both rank Bus over BF, & only the BF faction ranks BF over Bus, Bus pairbeats BF, with the maximal wv. Bus wins by pairbeating CW & BF. If CW is the largest faction (it’s the most likely to be the largest) & nothing else about the burial-result is known, then BF, by the most likely assumption, loses in all 3 scenarios, while Bus wins in the 3rd scenario. The method has autodeterence.