[EM] Condorcet for public proposals

[MIKE OSSIPOFF]

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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