[EM] Two round Condorcet / Improved TRS

[Abel Stan]

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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