[EM] Two round Condorcet / Improved TRS

[Chris Benham]

I find this complicated and very low bang-for-buck, and not properly 
defined  ("..a Smith method ").  I don't see any justification for 
privileging the FPP winner in this way.

The method (compared to better single-round methods) could give voters 
extra Burial and Compromise and Push-over incentives.  For example if 
your favourite is likely to be the CW (or Smith method winner) without 
your first-preference vote but unlikely to be the FPP winner, then you 
might gain by trying to change the (with you voting sincerely) FPP 
winner into one that is more likely to lose in the runoff.

If your favourite has less chance of being both the CW and the FPP 
winner than your lesser evil, you could have incentive to Compromise by 
voting Lesser Evil in first place to guard against a runoff that Greater 
Evil might win.

Supporters of the likely FPP winner will have a powerful incentive to 
Bury and Push-over at the same time.  They can use their below-top 
preferences to try to make any voted CW (who isn't also the FPP winner 
and their favourite) as less appealing as possible.

> "While even the paradigm of IRV retains this "few first preferences - 
> not legitimate" view, ..."

No. it works the way it does because there isn't any other way of fixing 
FPP's  failure of Clone-Winner while keeping compliance with 
Later-no-Help and Later-no-Harm.

If you like the idea of a method that can be thought of as a "compromise 
between 3 paradigms",  I recommend  Double Defeat, Hare:

*Voters strictly rank from the top however many candidates they wish and 
may also indicate an approval cutoff (possibly by ranking a "Approve 
none below" virtual candidate).

Any candidate pairwise beaten by a more approved candidate is 
disqualified.  Elect the not disqualified candidate that is highest 
ordered (that is the last to be eliminated or not eliminated) by Hare.*

That would be a high Social Utility (and high Condorcet consistency) 
method that is very resistant to Burial and losers' complaints.

Chris Benham

On 9/10/2024 6:56 pm, 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.
>
> 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.
>
> To the point: The classic top2 runoff is based on SNTV, and many 
> variants have been proposed. A major part not to forget is that the 
> second round is optional, an absolute majority of first preferences 
> avoids the second round. I think it has also been suggested that the 
> Condorcet winner should be the benchmark for this, and if there is 
> none, then a second round would be held.
>
> Here is my proposal (working titles: Improved TRS, 
> Condorcet-reinforced TRS, FPP+C or runoff):
> 1. If the first-preference plurality winner is also a Condorcet 
> winner, elect them.
> 2. If the first-preference plurality winner is not the CW but there is 
> a CW, they go to a runoff
> 3. If there is a tie for either, use a deterministic method to resolve 
> it, plurality tier resolved with an IRV (plurality elimination) based 
> system, no CW resolved with a Smith method.
>
> I think at first this may seem like there is no sense in it, since the 
> CW will win against the plurality winner if they are not the same. But 
> it is also meant to be improved TRS, not a single round system with 
> static preferences. So why might it be improved TRS?
>
> -In many cases, this will avoid a runoff entirely, where under TRS it 
> would have been held. A plurality is not enough to win outright, but 
> being the CW is still a lower bar than more than half of 
> first-preferences.
> -If voters do not change their preferences, it is of course a 
> Condorcet system, and equivalent to the system chosen to select the 
> second candidate in the runoff
> -It retains the aspects of TRS that make it different from contingent 
> voting and therefore appeals to both those who put some more emphasis 
> the potential second round being an election in its own right, after 
> an "unsuccessful" first one. In this sense it gives a majority vote 
> without tactics in the second round and a clear two-candidate choice. 
> Voters can inform themselves more between the two rounds.
> -Ties at any stage are of course "easier" to handle than under choose-one.
> -It increases trust in the election process from those sceptical of 
> any other paradigm than the first two, with more types of tactical 
> voting other than "lesser evil", who may fear an "illegitimate" CW. 
> While even the paradigm of IRV retains this "few first preferences - 
> not legitimate" view, here it can be tested. Since the plurality 
> winner is running up against a candidate who theoretically beat (or 
> was "closest" to beating) all others, it may be accepted that there is 
> no one better to challenge them in a 2 person race. This of course is 
> not the case, since plurality may have the worst loss against someone 
> other than the CW, but this already opens up more cans of worms.
>
> Of course, there are many potential downsides. This is a system 
> designed to be a compromise between 3 paradigms (but mainly the second 
> two, while superficially appealing to the first one too), so purists 
> of all can and will hate it. But it is also not meant to be analysed 
> strictly from a static point of view.
>
> 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?
>
> Best,
> Abel
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