Schulze & Ranked-Pairs(wv) have strong probabilistic autodeterrence of burial

[A Former User]

Schulze, RP(wv), MinMax(wv) & Smith//MinMax(wv) are all very strongly probabilistically-autodeterent.

I applied them to a typical example with a complete exhaustive set of 18 cases.

The test:

Factions& candidates:

The example is with 3 factions, respectively favoring 3 candidates: CW, BF, & Bus.

CW stands for sincere Condorcet winner (who is buried in the example’s 18 cases.

BF stands for Buriers’ Favorite.

Bus refers to the candidate under whom the buriers have buried the CW.

Basic example & its variables:

The 3 factions all differer in size, because in actuality they usually do.

But their sizes as nearly equal as nearly equal as possible, & their size difference is uniform.

…because that’s the center state of affairs about which the actual instances will vary…the most typical state of affairs (& probably most frequent state-of affairs, among all possible states of affairs).

Both the BF faction & the Bus faction prefer CW to eachother’s candidate.

The Bus faction ranks CW 2nd, because the examples are about ONE faction, the BF faction, attempting strategy.

The BF faction (insincerely) ranks Bus 2nd.

The CW faction, in the various cases, rank a 2nd choice of BF, Bus, or no one.

The 18 cases are for all 6 size-orderings for the 3 factions, & for all 3 ways for the CW faction to rank a 2nd choice (including no 2nd choice).

There are 99 voters.

e.g. the 1st case is:

32: CW>BF
34: BF>Bus
33: Bus>CW

The other cases cover all the combinations of the variations of the size-ordering variable & the CW faction’s2nd-choice variable.

The faction sizes of 34, 33, & 32 are used in all of the cases, in which the factions’ size ordering changes.

The measure of autodeterence is the ratio of the probability of electing Bus to the probability of electing BF.

…measured by the number of instances of the election of Bus, among the 18 cases, divided by the number of instances of the election of BF among those 18 cases.

So the measure of autodeterence in this test is:

Bus/BF…referring to the ratio of their numbers of wins among the 18 cases.

Results for Schulze, RP(wv), MinMax(wv), & Smith//MinMax(wv):

Bus/BF = 7.

Bus/BF when CW faction is smallest = 5.

Bus/BF when CW faction is middle = 5.

Bus/BF when BF faction is largest & CW faction is smallest = 2.

Bus/BF when BF faction is largest & Bus faction is smallest = 2.

Bus/BF when CW faction is largest is infinite (or undefined, because division by zero is undefined).

Offensive truncation wasn’t tested, because, for the above-named methods, it’s been well-known here for 35 years that offensive truncation doesn’t work when only one faction truncates, & the CW is supported by the other faction.

But, for any other method, of course the test would have to include an additional 18 cases of offensive truncation.

When I introduced Condorcet(wv), & told its properties, 35 years ago, they included compliance with what is now called the Minimal-Defense Criterion.

Because of the possibility of defensive truncation being used, that criterion-compliance conferred burial-deterrence.

But, even if defensive truncation isn’t used by enough voters, burial is nonetheless strongly deterred by those methods’ probabilistic autodeterence, described above.

Those methods are the only ones that have been determined to be probabilistically autodeterrent by exhaustive testing.

Given that Schulze & RP are widely popular & widely recognized as the kings of criteria-compliance, & given the extreme brevity possible for RP, RP(wv) is the obvious natural best proposal for a Condorcet-Criterion rang-method.

RP(wv):

If no voted CW (due to a top-cycle):

Drop the weakest defeat in every cycle.

Elect the resulting unbeaten candidate.

(Defeat-strength measured by number of ballots ranking defeater over defeated.)