[EM] Two round Condorcet / Improved TRS

[Kristofer Munsterhjelm]

On 2024-10-09 10:26, Abel Stan wrote:
> Hello everyone,
> 
> Lately I have been trying to informally survey the intuitions of people 
> not very familiar with voting methods. One of my tentative conclusions 
> was, that voting can be thought of in four major "paradigms", the first 
> of which I would call "choose-one" or "tribal" paradigm, then the 
> tempered version of this seen in "later-no-harm" systems (possibly an 
> intermediate paradigm), probably culminating in IRV/Hare, thirdly either 
> a broader group of some sort of "majority/compromise seeking" systems 
> (which would include Bucklin, score-median methods and just maybe, 
> approval too) or a narrower group of Condorcet systems and finally, the 
> cardinal/utilitarian paradigm. Probably this is not a very new way of 
> thinking about it, but maybe it is good context for what follows.

Strictly speaking, I don't think LNHarm directly translates to 
"uncompromising" or "tribal" methods. MMPO passes LNHarm, for instance, 
and it doesn't have the mostly uncompromising behavior of IRV.

The usual argument that LNH is uncompromising is something like: suppose 
we have an LCR election like this:

37: L>C>R
35: R>C>L
10: C>L>R

Then if C wins here, then L shouldn't win with

37: L
35: R>C>L
10: C>L>R

and because it seems obvious that in

37: L
35: R
10: C>L>R

either L or R should win, it also seems obvious that L must win in the 
second scenario. But there's another possibility: that the R-voters 
going to "R>C>L" flips the election from L to C. Then there's no LNHarm 
violation if the result stays at C when the L voters go from L to L>C>R.

That is (as far as I know) what MMPO does. When both the L- and R-voters 
plump, it elects L. When the R voters then do R>C>L, it elects C, which 
they prefer. Then the L-voters completing their ballots has no effect; C 
is still elected.

I get what you mean, though :-) Plurality, IRV, DAC, DSC; methods like 
those, with center squeeze. "Tribal" is not a too bad word for them.

> Of course, there are many systems outside or inbetween these four 
> paradigms. In fact, too the two-round system stands out as something 
> that the general public may have a different attitude on than simply the 
> social choice take. The two round system of course has the major 
> feature/bug of people being able to switch votes between the two rounds, 
> which aside from adding more tactical possibilities, also provides for 
> candidates/parties to make new endorsements and deals, while, in its 
> purest form it does provide a majority vote in the second round. The 
> only question is whether you look at the two rounds as one election, or 
> the first round as just candidate selection. Obviously, for most intents 
> and purposes, it should be viewed as one election, one system, but 
> because preferences voters information and preferences can genuinely 
> change between the two rounds, it is maybe not that simple.

Indeed not, and that may be part of the reason why top-two seems to lead 
to less two-party rule than IRV does. Top-two isn't just the contingent 
vote counted in a more complex manner.

(Finding a strategic voting model that distinguishes between the 
contingent vote and top-two would be interesting.)

> What do you think? In a strict theoretical sense, are there any 
> additional downsides/strategies other than that of the chosen base 
> Condorcet system and that it has the same added type of tactical voting 
> that TRS has ("strategic dynamic preferences")? Are there any other 
> systems you may think are better to combine this way, for a particular 
> application?

I imagine a second round would be the rule, not the exception. In a 
two-party system, the Plurality and Condorcet winners would stay the 
same; but as third parties become stronger, they will start drawing 
votes from the two parties, making Plurality increasingly unreliable as 
an indicator of candidate quality.

That is, the vote-splitting problems that lead to Duverger's law to 
begin with would start to resurface. The Condorcet component would make 
the method resist a return to two-party rule, and hopefully would 
prevent it entirely. But as long as we're in the multiparty domain, the 
Plurality scores may be arbitrarily off the Condorcet ones.

In an 1D spatial model, the contingent vote version of this method would 
lead the candidates to compete for the center. Plurality's 
vote-splitting/center squeeze would favor candidates further away from 
the center, but if they really are less popular than the center 
candidates, it wouldn't help them, as the second round would confirm the 
Condorcet candidate.

I can think of two ways that the top-two version could differ from the 
contingent vote version.

First, it could allow candidates to break out of a one-dimensional 
model. In 1D with honest voting, the median voter ("center") candidate 
is always the Condorcet winner. Candidates who can't compete with the 
center candidate on the given axis may try to create or draw attention 
to other axes to distinguish themselves. Suppose that the Plurality 
winner is such a "distinctive" candidate. Then debates between the round 
can more clearly highlight what this new axis corresponds to, which 
could lead the voters to change their minds, leading the Plurality 
winner to win the second round.

This dynamic exists in ordinary Condorcet methods as well, but the 
second round would bring the candidates' focus on different axes into a 
more clear light. Thus it could (possibly) make breaking out of 
two-party or one-dimensional politics easier.

Second, it could weaken the "weak centrist" or "milquetoast" objection. 
Suppose the Condorcet winner is a candidate who wins just by not making 
much of a fuss, serving platitudes instead of real policy; and suppose 
that the Plurality winner is a "tribally strong" candidate. Then in the 
run-up to the second round, the Plurality winner would try his hardest 
to expose the weak centrist by posing difficult questions. The weak 
centrist's non-responses could then weaken him so much that the voters 
switch to the Plurality winner in the second round.

I suspect that the weak centrist argument isn't as strong as it appears, 
because voters don't like sub-par candidates, and a wishy-washy 
candidate will seem like one. Being a weak centrist isn't a good look, 
and Condorcet methods, being able to pick up on slight preference 
differences, would punish this.

But it *is* an objection that has been made by "tribal system" 
proponents like FairVote. And having a second round would reduce the 
effect where it is significant, if it turns out I'm wrong.

If you want to maximize this check on weak centrists, IRV is probably a 
better choice than a Plurality; but that does make the system a lot more 
complex.

-km