In this method no candidate X can be eliminated without a direct democratic defeat from some competing candidate Y. Candidate X suffers a Direct Democratic Defeat from candidate Y iff a majority of the voters expressing a preference between them prefers Y over X. The best known eimination method being proposed today fails to respect this principle ... reserving Direct Democratic Defeat Elimination exclusively for the last candidate to be eliminated. Beyond the basic Direct Democratic Defeat Elimination (DDDE) requirement we need to invoken other criteria to establish the priority of elimination. Naturally we should eliminate the democratically weaker candidates before the democratically stronger candidates. One measure of democratic weakness is lack of democratic support in direct democratic comparison with other candidates. The democratic support for Y over X is the number of ballots that rank Y over X. We need a measure of the nominal over-all support of Y over the other competing candidates ... not just one of them. A natural candidate for such a measure is the Max democratic support for Y against the competing candidates. If that max support is small, then Y is generally democratically weak compared to candidates with larger max support. Beyond that this particular measure of weakness is uniqely helpful in preventing unscrupulous "sophisticated" voters from gaming the system ... and our method uses it in a way that makes the most insidious of those manipulations backfire on the manipulators. With that introduction, here's my most succinct formulation of Direct Democratic Defeat Elimination: If there is a candidate that suffers no direct democratic defeat from any competing candidate, elect that candidate. Otherwise ... Every remaining candidate suffers a direct democratic defeat ... so ... While every remaining candidate suffers a direct democratic defeat ... peatedly eliminate the democratically weakest remaining candidates (one by one, weakest first) along with any candidates that are too weak to defeat them. EndWhile You may wonder how there could be any candidate too weak to democratically defeat the nominally weakest candidate. It is possible because the general weakness of the nominally weakest candidate is just that ... a general weakness that may not correctly predict which candidate will prevail in every single Direct Democratic comparison. [But is much more reliable than IRV's general weakness measure (number of top votes) ... and unlike IRV ... we only eliminate with direct democratic corroboration.] For example, it can happen that the candidate Y whose max support is minimal, defeats some other candidate X that is democratically defeated by every other candidate, yet has a max support against Z larger than Y's max support against Z. So this "along with ..." clause serves to keep weak or "dark horse" candidates from escaping elimination... but more importantly to back-fire on the manipulators if there are any. The lay reader may want to skip over the next quite technical paragraph that shows precisely how the democratic structure of the elimination of "weakest along with those drmocratically defeated by wwakest" precipitates the back-fire against unscrupulous manipulators. [For example, if manipulating supporters of X down-ranked (what would have been) a sincere ballot set wiinner Y to create a rock-scissor-paper cycle in which the weakest democratic support was Y's against X ...that would backfire on the insincere down rankers... because Y would be the weakest support candidate in the cycle ... and would bring down X with it when eliminated.] That's all for now ... Any takers? If not, what part needs beefing up ... perhaps from being unclear or unconvincing? -Forest

Different implementations of the same election method (as an input/output system) may appeal to different people. If only people could understand that they truly were the same method (given that proveably they have the same output for the same input), they might worry less about the exact implementation before agreeing on the actual voting method. You might assume (as I once did) that the greater the variety of simple equivalent explanations of a method, the more support it would attract. But you would be wrong ... because people percieve different explanatiins of the same identical method as being competing incompatible voting methods. Having more ways to describe and explain a method ... instead of clearing up confusion ... is seen as the very source of confusion ... the old story of the blind men and the elephant. Paradoxically some of the same people assume that all methods based on RCV ballots must agree on who wins ... and that the only difference between such methods is the procedure for counting the ballots to find that winner ... more a matter of taste than anything else ... kind of the same way different Eastern religions look at different Western religions and vice-versa. People want one canonical voting procedure .... so that anything else is anathema! And too many people have already made up their minds that IRV is it. Heaven help us! On Wed, Mar 1, 2023, 6:07 PM Forest Simmons <forest.simmons21@gmail.com> wrote: > In this method no candidate X can be eliminated without a direct > democratic defeat from some competing candidate Y. > > Candidate X suffers a Direct Democratic Defeat from candidate Y iff a > majority of the voters expressing a preference between them prefers Y over > X. > > The best known eimination method being proposed today fails to respect > this principle ... reserving Direct Democratic Defeat Elimination > exclusively for the last candidate to be eliminated. > > Beyond the basic Direct Democratic Defeat Elimination (DDDE) requirement > we need to invoken other criteria to establish the priority of elimination. > > Naturally we should eliminate the democratically weaker candidates before > the democratically stronger candidates. > > One measure of democratic weakness is lack of democratic support in direct > democratic comparison with other candidates. > > The democratic support for Y over X is the number of ballots that rank Y > over X. > > We need a measure of the nominal over-all support of Y over the other > competing candidates ... not just one of them. > > A natural candidate for such a measure is the Max democratic support for Y > against the competing candidates. > > If that max support is small, then Y is generally democratically weak > compared to candidates with larger max support. > > Beyond that this particular measure of weakness is uniqely helpful in > preventing unscrupulous "sophisticated" voters from gaming the system ... > and our method uses it in a way that makes the most insidious of those > manipulations backfire on the manipulators. > > With that introduction, here's my most succinct formulation of Direct > Democratic Defeat Elimination: > > If there is a candidate that suffers no direct democratic defeat from any > competing candidate, elect that candidate. > > Otherwise ... > > Every remaining candidate suffers a direct democratic defeat ... so ... > > While every remaining candidate suffers a direct democratic defeat ... > peatedly eliminate the democratically weakest remaining candidates (one by > one, weakest first) along with any candidates that are too weak to defeat > them. > EndWhile > > You may wonder how there could be any candidate too weak to democratically > defeat the nominally weakest candidate. > > It is possible because the general weakness of the nominally weakest > candidate is just that ... a general weakness that may not correctly > predict which candidate will prevail in every single Direct Democratic > comparison. > > [But is much more reliable than IRV's general weakness measure (number of > top votes) ... and unlike IRV ... we only eliminate with direct democratic > corroboration.] > > For example, it can happen that the candidate Y whose max support is > minimal, defeats some other candidate X that is democratically defeated by > every other candidate, yet has a max support against Z larger than Y's max > support against Z. > > So this "along with ..." clause serves to keep weak or "dark horse" > candidates from escaping elimination... but more importantly to back-fire > on the manipulators if there are any. > > The lay reader may want to skip over the next quite technical paragraph > that shows precisely how the democratic structure of the elimination of > "weakest along with those drmocratically defeated by wwakest" precipitates > the back-fire against unscrupulous manipulators. > > [For example, if manipulating supporters of X down-ranked (what would have > been) a sincere ballot set wiinner Y to create a rock-scissor-paper cycle > in which the weakest democratic support was Y's against X ...that would > backfire on the insincere down rankers... because Y would be the weakest > support candidate in the cycle ... and would bring down X with it when > eliminated.] > > That's all for now ... > > Any takers? > > If not, what part needs beefing up ... perhaps from being unclear or > unconvincing? > > -Forest > >