If no majority approval in either round, then elect by random approval ballot from one or both rounds. [Draw as many as necessary to narrow down to one candidate] Kevin wrote ... I see a need for non-eliminative two-round methods. I like the idea that the first round places a "default winner" or "guy to beat" in the electorate's consciousness, so that, possibly, voters would consider offering more of their preferences in the second round. A difficult thing is to make sure it is worthwhile to seriously compete in the first round, and also, relatedly, that the second round should not simply reverse the outcome of the first round based on small changes in participation rate. Here's an idea based on two-round Approval. Let's call it NETRA. 1. If the first round winner ("FRW") has majority approval, he is elected. End. 2. Otherwise hold the second round with all the same candidates. If this new winner has majority approval *and* the FRW does *not* have majority approval, then the new winner is elected. Otherwise the FRW wins. So in the second round the FRW is given a couple of perks. If he raises his vote to a majority, or if (again) no one can get a majority, he doesn't have to beat anyone. He can prevail based on his first victory. This has two purposes: It should be desirable to be the FRW. And the FRW's advantage should increase the electorate's assessment of the FRW's odds, so that hopefully the second round serves to tell us whether there is a candidate preferred by the voters to the FRW. (It is an approval ballot in form, but what I'm actually after is the FRW's pairwise contests.) Main concerns: 1. If candidates were to conclude that being the FRW is overall a bad situation. I'm not sure how likely this is, given that a first-round majority is an auto-win. 2. It's still quite possible that a majority opposing the FRW in the second round would fail to agree to get behind any single candidate. Then a lack of an approval majority in the first round would simply be repeated in the second, for no benefit. (There is, I suppose, the additional confirmation, for all to see, that there is no majority willing to unite against the FRW... It also confirms that the winner couldn't attract a majority.)

Well, then if the majority fails to unite, they get better than 50/50 odds to defeat the FRW anyway. There may not even be a majority to unite. If the method collects 40 A, 35 B, 25 C twice in a row, maybe we just have three factions. I wouldn't want to throw a die and potentially elect C for example, in that case. Kevin Le dimanche 26 septembre 2021, 00:08:22 UTC−5, Forest Simmons <forest.simmons21@gmail.com> a écrit : > >If no majority approval in either round, then elect by random approval ballot from one or both rounds. > >[Draw as many as necessary to narrow down to one candidate] Kevin [earlier] wrote ... I see a need for non-eliminative two-round methods. I like the idea that the first round places a "default winner" or "guy to beat" in the electorate's consciousness, so that, possibly, voters would consider offering more of their preferences in the second round. A difficult thing is to make sure it is worthwhile to seriously compete in the first round, and also, relatedly, that the second round should not simply reverse the outcome of the first round based on small changes in participation rate. Here's an idea based on two-round Approval. Let's call it NETRA. 1. If the first round winner ("FRW") has majority approval, he is elected. End. 2. Otherwise hold the second round with all the same candidates. If this new winner has majority approval *and* the FRW does *not* have majority approval, then the new winner is elected. Otherwise the FRW wins. So in the second round the FRW is given a couple of perks. If he raises his vote to a majority, or if (again) no one can get a majority, he doesn't have to beat anyone. He can prevail based on his first victory. This has two purposes: It should be desirable to be the FRW. And the FRW's advantage should increase the electorate's assessment of the FRW's odds, so that hopefully the second round serves to tell us whether there is a candidate preferred by the voters to the FRW. (It is an approval ballot in form, but what I'm actually after is the FRW's pairwise contests.) Main concerns: 1. If candidates were to conclude that being the FRW is overall a bad situation. I'm not sure how likely this is, given that a first-round majority is an auto-win. 2. It's still quite possible that a majority opposing the FRW in the second round would fail to agree to get behind any single candidate. Then a lack of an approval majority in the first round would simply be repeated in the second, for no benefit. (There is, I suppose, the  additional confirmation, for all to see, that there is no majority willing to unite against the FRW... It also confirms that the winner couldn't attract a majority.) ---- Election-Methods mailing list - see https://electorama.com/em for list info