When I found out about BeatpathWinner's brief algorithm and computer program, I began recommending for committees, organizations, and polls. That was largely because the brief BeatpathWinner program was the only one that I'd written. I had diffriculty setting aside the time that it would take to write the much longer programs for SSD and Ranked-Pairs. So I was offering a BeatpathWinner program because that was all I had. People asked me where they could find a Ranked-Pairs program, and I had to say that I didn't know where they could find a wv RP program.
But all the time when I was recommending BeatpathWinner for committees, partly with the idea that the members of the committee, like me, would find a brief program more convenient, I was also saying that SSD, RP, and PC are the Condorcet versions to propose for public elections.
That's because those Condorcet versions are the ones with natural and obvious motivation and justification. Obviously, of those 3, PC isn't as good as the other 2.
CSSD and SSD differ in their stopping rule. SSD stops when someone is unbeaten. CSSD stops when there are no defeats among the candidates of the Schwartz set. When I initially suggested CSSD, no knowing about Markus's prior proposal, I was saying to stop when there are no cycles among the candidates of the current Schwartz set. When I heard about Markus's CSSD proposal, which worded the stopping rule in terms of defeats in the Schwartz set, instead of cycles, I adopted that wording, since defeats are a more natural notion than cycles. In that way, with CSSD, it's never necessary to mention cycles. Of course with SSD it's never necessary to mention cycles either.
Stopping the count when someone becomes unbeaten sounds much briefer, more natural, expected than stopping the count when there are no defeats among the candidates of the current Schwartz set. After all, the whole reason why a circular tie solution is needed was because initially no one was unbeaten. What could be more natural than to stop when someone becomes unbeaten.
As I was saying before, an innermost unbeaten set is compelling--It's obvious that the winner should come from that set. And that therefore the candidates of that set are the ones who should have their defeats dropped.
Here's how I define SSD:
Schwartz set definition:
1. An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set.
2. An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set.
3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.
SSD:
1. If any candidate is unbeaten, they win and the count ends.
2. Otherwise, determine which candidates are in the Schwartz set, counting only undropped defeats.
3. Drop the weakest defeat among the members of that set. Go to 1.
[end of SSD definition]
Ranked-Pairs is also obviously motivated and justified, and that makes it too a good proposal for public elections. Its definition is probably briefer than that of SSD, because SSD requires the Schwartz set to be defined. But RP loses some of its brevity when its midcount-tie-solution is specified.
Ranked-Pairs:
To "keep" a defeat means to record it as being kept.
In order of strongest defeats first, consider each defeat in turn as follows: Keep it doesn't conflict with already-kept defeats, by being in a cycle with them-- i.e., by being in a cycle consisting only of it and some already-kept defeats.
When all the defeats have been considered in that way, a candidate wins if s/he has no kept defeats.
[end of RP definition]
Ranked-Pairs isn't a descriptive definition. If it applies to RP at all, it could also apply to some other Condorcet versions. Steve Eppley has suggested a better name:
Maximize Affirmed Majorities (MAM). That name well describes what MAM does.
RP can have midcount ties, situations where there are 2 or more equally strongest as-yet unconsidered defeats. The problem is, which one should be considered first? It's said that, for the purpose of clone-independence and monotonicity, maybe the best way to solve that is to randomly chose the order in which to consider them. That doesn't sound like something that the public would like, however.
I suggested an RP midcount tie solution on this mailing list some time ago. It's based on the idea that a defeat is nullified if it's in a cycle with defeats that are all at least as strong as it is:
1. Call the equally strongest as-yet unconsidered defeats the "tie defeats".
2. Defeats that were kept before keeping any tie defeats are called "old defeats".
3. A tie defeat is "qualified" if it isn't in a cycle consisting only of it and some old defeats.
4. Keep every qualified tie defeat that is not in a cycle each of whose members is either an old defeeat or a qualified tie defeat.
[end of "deterministic1" midcount tie solution definition]
In the EM discussion at that time, it was called deterministic1. Steve had already considered it.
I thought that was the brief midcount tie solution, till Eric suggested something briefer:
[using the same definitions as before]
Keep every tie defeat that isn't in a cycle consisting only of it and some old defeats.
[end of briefer midcount tie solution]
That's so much briefer that I immediately agreed that that's the one to offer for public proposals.
It could probably be worded so that it wouldn't be necessary to separately define tie defeats and old defeats.
In public elections, equal defeats are so rare that it doesn't reallly matter what the rule is for solving them. Brevity is all-importnat, and the brief midcount tie solution is the one to include in public MAM proposals.
As I've often said, the merit difference between MAM and SSD in public elections is negligible. The choice between those two should be based entirely on which is more likely to be accepted. Maybe a "focus group" public meeting or a poll should be done to chose.
If I was proposing only BeatpathWinner/CSSD for committees only because it was the only one that I had a count program written for, maybe that isn't the best way to choose a voting system. Maybe RP should be considered as a method for committees. Maybe a program should be written that implements CSSD by its own very plausible definition, rather than by BeatpathWinner. For a committee, the choice between CSSD and CSSD would obviously depend on whether an obvious stopping rule is more imporant than clone independence. Will clone advantage or disadvantage really happen often enough to cause factions to strategically introduce clones? I doiubt it.
As I said, it's been suggested that the MAM midcount tie solutions that I described might not be clone-independent &/or monotonic. How much of a problem is that? How likely is a faction to strategically run (or avoid) clones, on the chance that there will be equal defeats, in circumstances that favor or disfavor clones? Probably not so likely. How likely is someone to downrank his favorite so as to make him win in the unlikely event that a certain two defeats will be equal, and the other circumstances will be right for that particular candidate to benefit from the nonmonotonicy and from that voter's downranking strategy. It doesn't sound real likely, does it.
I've had good response to an SSD definition. SSD doesn't require any mention of cycles. MAM requires at least mention of defeats that conflict or are incompatible, etc. Someone might ask how defeats conflit, and then you're defining cycles to that person. With SSD you never have to speak of cycles, or incompatible defeats.
But SSD and MAM are both excellent public Condorcet proposals.
Sometimes we underestimate how resistant people might be to anything whose definition is longer than a line or two. Sure, anyone who is willilng to read the definitions of SSD and MAM will like them. But what about all those people who will reject them without being willing to read the definition, because they consider a short paragraph to be too long? For them, maybe Condorcet is a better idea.
Sure SSD & MAM are better, but if people insist on something more briefly-defined, them Plain Condorcet (PC) is the thing:
If anyone is undefeated they win. Otherwise drop the weakest defeat. Repeat till someone is undefeated. They win.
[end of PC definition]
PC is called Basic Condorcet at the electionmethods website.
Sure, PC violates Condorcet Loser. But it would happen only rarely. It would be a peculiarly popular Condorcet loser who has fewer people preferring anyone else to him than anyone else does.
If a Condorcet Loser wins it would be an embarrassment. But the likely "badness" of that winner is reduced by the fact that he has the fewest people preferring anyone else to him.
Condorcet Loser could also be used against PC in campaigns, and that objection would have to be answered. For one thing, Condorcet Loser can't be used to oppose replacing Plurality with PC, because Plurality violates it too, probably more often.
Keep thiis in persepctive. Let's not exaggerate how likely or how much of a problem PC's ability to fail Condorcet Loser is.
Mike Ossipoff
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