Two round Condorcet / Improved TRS
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):
- If the first-preference plurality winner is also a Condorcet winner,
elect them. - If the first-preference plurality winner is not the CW but there is a
CW, they go to a runoff - 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
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
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):
- If the first-preference plurality winner is also a Condorcet
winner, elect them. - If the first-preference plurality winner is not the CW but there is
a CW, they go to a runoff - 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
Election-Methods mailing list - see https://electorama.com/em for list info
On 2024-10-12 03:24, Chris Benham wrote:
"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.
Do you mean that it's the only method that can have those three
properties, or that it's the only FPP-based method?
If the latter, it would be interesting to know (in a theory sense) if
there exists a method that passes all three and has fewer strategic
nomination problems than IRV.
-km
I am a bit rusty with these thought experiments, but I think I mean the
former. That is, something other than Hare that meets Clone-Winner and
both LNHarm and LNHelp is a tall order.
I suppose one could try to interpret Approval as FPP(ER-Whole) and try
to claim that it meets Later-no-Harm just like plain FPP, but I find
that obviously perverse
and wrong.
I'm not very concerned about Hare's (aka IRV's) alleged "strategic
nomination problems".
Chris B.
On 12/10/2024 8:24 pm, Kristofer Munsterhjelm wrote:
On 2024-10-12 03:24, Chris Benham wrote:
"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.
Do you mean that it's the only method that can have those three
properties, or that it's the only FPP-based method?
If the latter, it would be interesting to know (in a theory sense) if
there exists a method that passes all three and has fewer strategic
nomination problems than IRV.
-km