Re: [EM] Quick and Clean Burial Resistant Smith
On 15.01.2022 21:50, Richard, the VoteFair guy wrote:
Yet I believe that lots of audience members would give more trust to a
method that eliminates candidates one at a time. This is the simplicity
advantage that instant-runoff voting (IRV) has. In contrast, starting
with the Copeland winner might seem like magic to people who fear math.
Would eliminating from the bottom always work?
In the Wikipedia example below, it does work. It identifies B and E as
outside the Smith set, so the remaining candidates are in the Smith set.
5 wins for A
5 wins for D
4 wins for G
3.5 wins for C
2.5 wins for F
1 win for B
0 wins for E
(Half indicates a tie.)
So, my question is: Does elimination from the bottom always work?
My guess is the answer is yes.
I think so too, in theory. Suppose that A is in the Smith set and B is
not. Then A beats everybody who B beats and then some. So B will be
ranked below A by Copeland score. Hence the only way someone in the
Smith set will at the bottom of the list is if everybody is in it.
But you still need to decide when to stop, which can be pretty
difficult. At first it'd seem to be obvious: if the bottom-most
candidate beats anyone else pairwise, he'd be in the Smith set, no? But
that doesn't quite work. Consider something like this:
The candidates are ABCD. There's a Condorcet winner, A, who beats
everybody. But there's also a loser three-cycle, B>C>D>B. Thus whoever
you choose to eliminate first of B, C, and D, that candidate beats
someone else despite being outside the Smith set. And batch-eliminating
everybody with an identical least score fails in more complicated scenarios.
To justify the Copeland winner being the initial candidate, I would just
point to the reasoning above: any non-Smith set member beats or ties
fewer people than every Smith set member (almost by definition). So the
topmost by number of candidates beaten can't be outside the Smith set.
If the voters are expected to know what a Smith set is, that leap
shouldn't be too large. And if not, then every Smith//X method will look
like magic to some degree. (Better use Benham or BTR-STV.)
-km
On Sat, Jan 15, 2022 at 5:54 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
I've at times thought that a more realistic approach would be to use
evolutionary stable strategies, e.g. suppose everybody is honest, then
some small faction defecting can't grow in power to the point where
everybody feels the need to vote tactically. But that's even harder to
model, and some societies are used to tactical voting at the start (e.g.
US Plurality elections), and might thus not fit that very well.
It would be a bit hard to model, but one could imagine allowing the
electorate to run the election many times and adjust their strategy, but
insert the assumption that if a voter will not get a better outcome by
being strategic, they'll choose to be honest. So you could model whether an
electorate that starts out with strategy evolves toward honesty.
Now I'm wondering if the strategically resistant methods mainly increase
their resistance by making it impossible for trivial strategy to work in
cases where it would otherwise work. From my experimentation, I've found
out that reversal symmetry usually makes for a susceptible method, and
that rev. sym. and Condorcet together are incompatible with dominant
mutual third burial resistance.
This really got me curious. I've been reading up on these concepts and I
saw that you posted a proof of this in 2018. I still need to wrap my head
around these concepts. For example, it's not intuitively obvious to me why
reversal symmetry is important. If the voters are split into two equal
camps:
Camp 1: Loves A, tolerates B, hates C
Camp 2: Loves C, tolerates B, hates A
It's easy to see B as the right compromise winner, and if you reverse the
preferences that wouldn't change.
Similar reasoning can be found in https://rangevoting.org/WVmore.html
which seems to argue that DH3 is a problem even for Condorcet methods
that pass DMTBR (like Smith//IRV, Benham, etc):
The wiki says that "a method that passes DMTBR is immune to electing the
dark horse", but I can easily devise a pathological example where the dark
horse is the Condorcet winner:
9: A > X > B > C
7: B > X > C > A
5: C > X > A > B
So I assume that the wiki most be defining Dark Horse in a narrower sense
than how I'm reading it.
In any case, as you say, strategy-resistant methods like the Smith-IRV
hybrids will reduce the chance that strategy works, and so would give
third parties some more room in which to grow.
It would be interesting to do a test with Range; I imagine that it would
be very susceptible to strategy, similar to Approval. And I would also
imagine that STAR would do considerably better.
I just implemented Range and STAR and it seems that Range is indeed very
susceptible but STAR is not much better. I had to make some arbitrary
choices when implementing the scoring system. I made the score proportional
to the negative distance between a voter and each candidate, normalized to
span the 0-5 range. So every voter uses the entire 0-5 range, regardless of
whether they feel strongly about their preferences or not. I imagine that's
how most voters would behave. I chose a 0-5 range because that's what STAR
seems to use. I also had to make some decisions on how to implement each
strategy for a score ballot:
-
For the trivial strategy, I give c_k a score of 5 and w_A a score of 0,
and leave other scores the same. -
For the reverse strategy, I compute the ballot that w_A would have cast,
I "reverse" the scores with "new_score = 5 - old_score". Then give a score
of 5 to c_k and a score of 0 to w_A. -
For the moderate strategy, where I try every possible ranked ballot, I
was forced to find a way to convert a ranked ballot into a set of scores. I
decided to spread the scores uniformly from 0 to 5, so it's as if each
preference is equally strong.
N_elections = 20,000
N = 4, V = 99, C = 5
Method , 95% c.i. , trivial, reverse, moderate, majority
MiniMax , 0.4019-0.4155, 0.895 , 0.0805 , 0.02447 , 0.219
Hare , 0.0683-0.0752, 1.000 , 0.0000 , 0.00000 , 0.135
Benham , 0.0470-0.0528, 0.979 , 0.0160 , 0.00502 , 0.132
Smith_IRV, 0.0474-0.0532, 0.944 , 0.0169 , 0.03888 , 0.137
Range , 0.7828-0.7935, 0.832 , 0.1012 , 0.06667 , 0.601
STAR , 0.7485-0.7621, 0.620 , 0.0775 , 0.30275 , 0.522
The 95% interval for Range is very close to the susceptibility that JGA
reports on Table 1 (not identical; he probably computed scores
differently). STAR adds very little protection from strategy. Both systems
are extremely susceptible to manipulation. STAR requires the most complex
strategies, but that should give us no comfort; the two score systems
succumb to the simplest strategy more often than other systems succumb to
any strategy at all.
STAR: 75% susceptible x (62% trivial + 8% reverse) = 52%
Benham: 5% susceptible x (98% trivial + 1.6% reverse) = 5%
Cheers,
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
A bit of a side question, but is strategy resistance a good metric to quote?
FIrstly, you'd never rank methods on it - you'd end up choosing a
coin toss.
Secondly, voting methods recommended for their resistance to
tactical voting sometimes have the property that when they go wrong,
they make larger mistakes than those made by methods targeting sincere
voting. If you don't take this into account, you can draw misleading
conclusions.
Thirdly, consider a 3-candidate election using IRV. The central
candidate is the Condorcet winner, but supporters of one of the
non-central candidates realise that the opposed non-central candidate is
likely to win owing to the operation of a centre squeeze, and therefore
compromise on the central candidate. This satifies JGA's definition of
strategic manipulation but is certainly not an additional fault in IRV;
on the contrary, it's a mitigation of its weakness under sincere voting.
My own practice has been to measure the performance of methods in the
presence of tactical voting exactly as I would in its absence, simply
skipping over any attempted manipulation which doesn't lead to a worse
result.
CJC
On Mon, Jan 17, 2022 at 2:48 AM Colin Champion
colin.champion@routemaster.app wrote:
A bit of a side question, but is strategy resistance a good metric to
quote?
FIrstly, you'd never rank methods on it - you'd end up choosing a
coin toss.
It's not my #1 priority, but it seems pretty important to me. Given a
choice between two methods that are equally good in other respects, I would
pick the one where the best strategy is to vote honestly. It's hard to
trust that an otherwise good voting method will produce good results if
people are motivated to lie on their ballots.
Secondly, voting methods recommended for their resistance to
tactical voting sometimes have the property that when they go wrong,
they make larger mistakes than those made by methods targeting sincere
voting. If you don't take this into account, you can draw misleading
conclusions.
Hmmm... I did not know that. Can you give me an example? Yeah, that sounds
like something we'd really want to avoid.
Thirdly, consider a 3-candidate election using IRV. The central
candidate is the Condorcet winner, but supporters of one of the
non-central candidates realise that the opposed non-central candidate is
likely to win owing to the operation of a centre squeeze, and therefore
compromise on the central candidate. This satifies JGA's definition of
strategic manipulation but is certainly not an additional fault in IRV;
on the contrary, it's a mitigation of its weakness under sincere voting.
That does sound like a fault in IRV. If the goal is to get the Condorcet
winner (and I agree!) why not use a Condorcet method? The example you cite
is one of my biggest complaints with IRV. If people are driven to vote
dishonestly to compensate for a failure of the system, that tells me that
the method is flawed.
My own practice has been to measure the performance of methods in the
presence of tactical voting exactly as I would in its absence, simply
skipping over any attempted manipulation which doesn't lead to a worse
result.
If two election methods elect the same good candidate, but one of them
achieves that by letting people vote honestly and the other requires people
to learn that they need to manipulate their votes... to me that seems like
a relevant difference.
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
Daniel wrote:
Given a choice between two methods that are equally good in other
respects, I would pick the one where the best strategy is to vote
honestly. It's hard to trust that an otherwise good voting method will
produce good results if people are motivated to lie on their ballots.
This is a valid point. My own metric implicitly assumes that an innocent
error is neither more nor less serious than an error induced by tactical
voting. This is a reasonable starting position but not ultimately
tenable - ideally we'd want to weight the two sorts of error
differently, and recognise that providing people with an incentive to
vote dishonestly is an additional fault besides getting the wrong
result. But a weight of 0 for innocent errors is even less tenable, and
if we're to quote a single figure we can't avoid adopting some implicit
weight.
In fact even innocent errors aren't really innocent. If a method
produces errors which aren't due to tactical voting, they're probably
due to the configuration of candidates, and therefore provide perverse
incentives to candidacy which in turn distort political discourse. In
the end I've been inclined to stick with equal weighting while admitting
that it needs a prominent health warning, but this is partly because
I've never seen the position argued that tactical errors are more
critical than innocent ones.
On the magnitude of errors, my own figures suggest that Condorcet/Hare
makes fewer but larger errors than minimax when confronted with false
cycle tactics, and therefore looks marginally better in terms of
accuracy (and no doubt much better in terms of strategy resistance) but
significantly worse in terms of Euclidean loss. See
http://www.masterlyinactivity.com/condorcet/condorcet.html#results
(where Condorcet/Hare=Condorcet+AV).
And on IRV... I don't favour it at all, but having condemned it for its
faults, I don't want to additionally condemn it for its few merits, one
of which is allowing a strategic escape from the centre squeeze.
CJC
On 17/01/2022 09:31, Daniel Carrera wrote:
On Mon, Jan 17, 2022 at 2:48 AM Colin Champion
colin.champion@routemaster.app wrote:
A bit of a side question, but is strategy resistance a good metric
to quote?
FIrstly, you'd never rank methods on it - you'd end up choosing a
coin toss.
It's not my #1 priority, but it seems pretty important to me. Given a
choice between two methods that are equally good in other respects, I
would pick the one where the best strategy is to vote honestly. It's
hard to trust that an otherwise good voting method will produce good
results if people are motivated to lie on their ballots.
Secondly, voting methods recommended for their resistance to
tactical voting sometimes have the property that when they go wrong,
they make larger mistakes than those made by methods targeting
sincere
voting. If you don't take this into account, you can draw misleading
conclusions.
Hmmm... I did not know that. Can you give me an example? Yeah, that
sounds like something we'd really want to avoid.
Thirdly, consider a 3-candidate election using IRV. The central
candidate is the Condorcet winner, but supporters of one of the
non-central candidates realise that the opposed non-central
candidate is
likely to win owing to the operation of a centre squeeze, and
therefore
compromise on the central candidate. This satifies JGA's
definition of
strategic manipulation but is certainly not an additional fault in
IRV;
on the contrary, it's a mitigation of its weakness under sincere
voting.
That does sound like a fault in IRV. If the goal is to get the
Condorcet winner (and I agree!) why not use a Condorcet method? The
example you cite is one of my biggest complaints with IRV. If people
are driven to vote dishonestly to compensate for a failure of the
system, that tells me that the method is flawed.
My own practice has been to measure the performance of methods in the
presence of tactical voting exactly as I would in its absence, simply
skipping over any attempted manipulation which doesn't lead to a
worse
result.
If two election methods elect the same good candidate, but one of them
achieves that by letting people vote honestly and the other requires
people to learn that they need to manipulate their votes... to me that
seems like a relevant difference.
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
On 17.01.2022 09:48, Colin Champion wrote:
A bit of a side question, but is strategy resistance a good metric to
quote?
It's a good metric "all other things equal". I agree that it's not a
good metric by itself since, as you point out, the strategy-proof
methods (random ballot, random pair) are not particularly good in
practice as you end up giving up too much to resist strategy.
We could get a better image by considering both the resistance to
strategy and the honest voting performance (in the form of VSE for the
particular distribution that was chosen). We'd then get a Pareto front
that shows just how bad a method has to get under honesty to resist this
much strategy.
Some methods would simply be Pareto-dominated: I think IRV would be
dominated by the Condorcet-IRV hybrids because the latter both have
better honest performance when there is a CW, and better strategy
resistance (due to Condorcet fixing much of IRV's compromise incentive).
It's true that some methods work better under strategy than with
honesty. While I think the strategy measure may be somewhat misleading
in such a case, I think that it still indicates that the method isn't
optimal.
The reason is related to the revelation principle. Suppose that method X
does poorly with honest results but pretty good with strategy. Then we
can construct another method, DSV-X, that executes this strategy on
behalf of the honest voters. DSV-X will be better on honest than X by
our initial assumption. In addition, the algorithm inside DSV-X will
have full information of the ballots and so can potentially execute even
better strategies than the voters can do with imperfect information.
Thus the failure of X to itself do so (and the voters to have to do it
instead) is a flaw of the method X, and DSV-X (or some other method that
patches the problem) should be used instead.
(This is part of my beef with Range: it expects the voters to perform
some kind of strategy to cover for its shortcomings, and if the voters
misjudge the strategy things can go very wrong. And because there's no
unambiguous honest vote, its advocates tend to not consider this kind of
voting strategic in the first place.)
A true utilitarian might say that instead of recording the number of
elections where it's possible to strategize, we should separately record
the mean max loss (i.e. mean of worst loss that can come from
strategizing, over every election with strategy), mean expected loss,
mean maximum gain (as an indicator of when it might be better to replace
the method with a DSV one), and variance.
While I can see that point, there's something I like about just
recording the raw count: it's sort of a precautionary approach, that
strategy could be bad so we better avoid it. One could make a number of
arguments that utility calculations don't show the full picture: e.g.
suppose a method incentivizes two-party rule but has pretty good
(utility) performance once multiple parties are viable. Then the latter
is of less importance because you can't easily get there. Trying to
eliminate as many venues for strategy as possible should reduce the
chance of such problems happening.
-km
On 17.01.2022 08:36, Daniel Carrera wrote:
On Sat, Jan 15, 2022 at 5:54 PM Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> wrote:
I've at times thought that a more realistic approach would be to use
evolutionary stable strategies, e.g. suppose everybody is honest, then
some small faction defecting can't grow in power to the point where
everybody feels the need to vote tactically. But that's even harder to
model, and some societies are used to tactical voting at the start (e.g.
US Plurality elections), and might thus not fit that very well.
It would be a bit hard to model, but one could imagine allowing the
electorate to run the election many times and adjust their strategy, but
insert the assumption that if a voter will not get a better outcome by
being strategic, they'll choose to be honest. So you could model whether
an electorate that starts out with strategy evolves toward honesty.
Yes. Perhaps let each voter vote strategically with some probability p,
and if the strategy worked, p increases. It's a bit tricky because most
methods are nonresponsive to just a few ballots changing.
Now I'm wondering if the strategically resistant methods mainly increase
their resistance by making it impossible for trivial strategy to work in
cases where it would otherwise work. From my experimentation, I've found
out that reversal symmetry usually makes for a susceptible method, and
that rev. sym. and Condorcet together are incompatible with dominant
mutual third burial resistance.
This really got me curious. I've been reading up on these concepts and I
saw that you posted a proof of this in 2018. I still need to wrap my
head around these concepts. For example, it's not intuitively obvious to
me why reversal symmetry is important. If the voters are split into two
equal camps:
Camp 1: Loves A, tolerates B, hates C
Camp 2: Loves C, tolerates B, hates A
It's easy to see B as the right compromise winner, and if you reverse
the preferences that wouldn't change.
In this scenario, for a rev. sym. obeying method, if the camps are
equally large, there's a three-way tie; otherwise the majority wins. So
reversal symmetry implies some kind of additional structure; in this
case that it can't be too compromise-friendly. And apparently this
structure then precludes certain types of strategy resistance, though I
have no idea why, as my proof is one of exhaustion.
The wiki says that "a method that passes DMTBR is immune to electing the
dark horse", but I can easily devise a pathological example where the
dark horse is the Condorcet winner:
9: A > X > B > C
7: B > X > C > A
5: C > X > A > B
So I assume that the wiki most be defining Dark Horse in a narrower
sense than how I'm reading it.
Yeah, the point is that suppose a Dark Horse initially has no support,
i.e. actually is a universally loathed candidate. Then he's outside of
the innermost DMT set, and DMTBR says that voters who prefer A to the
current winner W can't make A win by burying W under someone who isn't
in the innermost DMT set. So the A-first voters have no incentive to
bury under the dark horse. Thus the ball doesn't get rolling and there's
no escalation into a chicken problem.
Warren then says "perhaps that won't save you because people will bury
blindly anyway". Which is something I don't agree with. Sometimes I get
the impression he draws too much experience from Borda, which is awful.
In any case, as you say, strategy-resistant methods like the Smith-IRV
hybrids will reduce the chance that strategy works, and so would give
third parties some more room in which to grow.
It would be interesting to do a test with Range; I imagine that it would
be very susceptible to strategy, similar to Approval. And I would also
imagine that STAR would do considerably better.
I just implemented Range and STAR and it seems that Range is indeed very
susceptible but STAR is not much better. I had to make some arbitrary
choices when implementing the scoring system. I made the score
proportional to the negative distance between a voter and each
candidate, normalized to span the 0-5 range. So every voter uses the
entire 0-5 range, regardless of whether they feel strongly about their
preferences or not. I imagine that's how most voters would behave.
I agree that's a realistic approach. Incidentally, normalizing the
ballots (which voters would most likely do to make use of the entire
range) means that a Range election outcome can change if losing
candidates enter or leave the race, even though Range strictly speaking
passes IIA.
I chose a 0-5 range because that's what STAR seems to use. I also had to
make some decisions on how to implement each strategy for a score ballot:
-
For the trivial strategy, I give c_k a score of 5 and w_A a score of
0, and leave other scores the same. -
For the reverse strategy, I compute the ballot that w_A would have
cast, I "reverse" the scores with "new_score = 5 - old_score". Then give
a score of 5 to c_k and a score of 0 to w_A. -
For the moderate strategy, where I try every possible ranked ballot,
I was forced to find a way to convert a ranked ballot into a set of
scores. I decided to spread the scores uniformly from 0 to 5, so it's as
if each preference is equally strong.
N_elections = 20,000
N = 4, V = 99, C = 5
Method , 95% c.i. , trivial, reverse, moderate, majority
MiniMax , 0.4019-0.4155, 0.895 , 0.0805 , 0.02447 , 0.219
Hare , 0.0683-0.0752, 1.000 , 0.0000 , 0.00000 , 0.135
Benham , 0.0470-0.0528, 0.979 , 0.0160 , 0.00502 , 0.132
Smith_IRV, 0.0474-0.0532, 0.944 , 0.0169 , 0.03888 , 0.137
Range , 0.7828-0.7935, 0.832 , 0.1012 , 0.06667 , 0.601
STAR , 0.7485-0.7621, 0.620 , 0.0775 , 0.30275 , 0.522
Note that a majority winner doesn't make either Range or STAR
unmanipulable. So that could be (part of) the reason you're getting
different results to JGA.
Also, using every possible rated ballot instead of ranked might
slightly improve the moderate strategy.
I'm surprised that STAR is such a poor performer, though! (How about
IRNR_p? This is IRV-style elimination of the loser, except after each
step, the original rated ballot has the eliminated candidates removed
and then the ballot is rescaled to have unit p-norm. Try p=1,2,infinity.)
I guess the hunt's still on for a cardinal method that really resists
strategy. There's Hay voting, which is a strategyproof method (under VNM
utilities), but it has predictably awful honest performance, just like
Random Ballot has in the ranked domain.
-km
On Mon, Jan 17, 2022 at 4:29 AM Colin Champion
colin.champion@routemaster.app wrote:
On the magnitude of errors, my own figures suggest that Condorcet/Hare
makes fewer but larger errors than minimax when confronted with false cycle
tactics, and therefore looks marginally better in terms of accuracy (and no
doubt much better in terms of strategy resistance) but significantly worse
in terms of Euclidean loss. See
http://www.masterlyinactivity.com/condorcet/condorcet.html#results
(where Condorcet/Hare=Condorcet+AV).
Thanks for the link. I'm going to need time to digest all of that. I just
updated my program to compute the Eucledian loss. I'm sure I can't compare
my numbers to yours; there will be a lot of implementation differences, and
you implement a lot more strategies than I do. But here it goes anyway:
Method , suscep, new winner is ...
MiniMax , 0.412 , better=0.134, worse=0.866
Hare , 0.066 , better=0.655, worse=0.345
Benham , 0.047 , better=0.135, worse=0.865
Smith_IRV, 0.047 , better=0.120, worse=0.880
Range , 0.787 , better=0.072, worse=0.928
STAR , 0.750 , better=0.061, worse=0.939
The first column ("suscep") is how often the method is susceptible to
strategy. It's basically the same number I've been posting here lately. The
next two numbers tell you how often the new winner (i.e. after strategy) is
better (i.e. smaller Eucledian distance to the mean voter) or worse than
the original winner. I was surprised to see that with Hare / IRV tactical
voting actually seems to make candidates better. I wonder how many of those
would be similar to the centre squeeze scenario you were just telling me
about. For other methods, strategy seems to be universally unhelpful.
Here is the Eucledian loss (gain?) for each case:
Method , Change in Eucledian distance
MiniMax , better=0.067, worse=0.196
Hare , better=0.157, worse=0.172
Benham , better=0.081, worse=0.228
Smith_IRV, better=0.081, worse=0.241
Range , better=0.077, worse=0.355
STAR , better=0.068, worse=0.335
The units are a bit different from yours. The mean voter is at a distance
~2.0 from the center, and ditto for candidates. Overall, these don't look
like very big jumps in either direction. That said, for all systems except
Hare, the downside of using strategy is significantly greater than the
upside.
You said that Condorcet/Hare makes fewer but larger errors than minimax
when confronted with false cycle tactics. I cannot confirm that because I
have not implemented false cycle tactics. But for the strategies I have
implemented, they look pretty similar.
Cheers
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
Hi Kristofer,
Le samedi 8 janvier 2022, 17:21:22 UTC−6, Kristofer Munsterhjelm km_elmet@t-online.de a écrit :
I have a hunch that if you put your "strategy-resistant Condorcet" hat on and
evaluate C//FPP, you will find it to be "good."
In my Monte Carlo (non-exhaustive) simulations, there are generally
three types of methods as far as strategy resistance goes: the type
that's susceptible >90% of the time whatever the number of candidates,
the type that's ~30% but increases with number of candidates to very
high levels with lots of candidates, and the type that's low and doesn't
increase.
A method is susceptible to strategy in a particular election if the
honest winner is A but voters who prefer some other B to A can conspire
to get B elected by changing their ballots.
C//FPP is the first type. MAM, Schulze, minmax, etc are of the second
type, and Smith-IRV, Benham, and fpA-fpC are of the third type.
Each election is a one-shot game (first some candidate wins, then
factions get to try to make other candidates win); there's no defensive
strategy. So it probably resembles your "never looks attractive in the
first place" setting.
Interesting. I suppose the obvious burial scenario for C//FPP is just every
single scenario where there's a CW who is not the FPW.
From scenarios I've been able to generate, it seems to me that fpA-fpC is purely
a middle ground between C//FPP and C//IRV. (Looking at three candidates.) I have
not, I think, seen a scenario where fpA-fpC, in a cycle, elects the FP loser, or
elects a non-FPW who didn't beat the FPW pairwise.
In other words, fpA-fpC usually likes the C//FPP winner, but sometimes it
prefers the second-place first preference candidate, provided they beat the
first preference winner. (Incidentally, my proposed expansion to fpA-fpC doesn't
maintain this pattern...)
It surprises me that you measure C//FPP to be in a whole other category, of
high manipulability, when in "method space" it is so close to those third type
methods.
I wonder how you categorize BPW and SV? I find them to be quite distant in
method space from those third type methods. But by my strategy measures they
seem attractive, with less compromise and burial incentive. The truncation
performance is comparable/mixed. It's just mono-raise and mono-add-top where BPW
and SV look unusually bad.
If you would want a 4+ candidate version of BPW (for example in order to
determine whether it is "second type"), you can use "first preference chain
climbing." Start with an empty set. Go down the list of candidates sorted by
first preference count, descending. When a candidate beats all candidates (if
any) in the set, add them to the set. Elect the last candidate you can add.
Kevin
On 01/17/2022 4:31 AM Daniel Carrera dcarrera@gmail.com wrote:
On Mon, Jan 17, 2022 at 2:48 AM Colin Champion colin.champion@routemaster.app wrote:
A bit of a side question, but is strategy resistance a good metric to quote?
FIrstly, you'd never rank methods on it - you'd end up choosing a
coin toss.
...
Thirdly, consider a 3-candidate election using IRV. The central
candidate is the Condorcet winner, but supporters of one of the
non-central candidates realise that the opposed non-central candidate is
likely to win owing to the operation of a centre squeeze, and therefore
compromise on the central candidate. This satifies JGA's definition of
strategic manipulation but is certainly not an additional fault in IRV;
on the contrary, it's a mitigation of its weakness under sincere voting.
That does sound like a fault in IRV. If the goal is to get the Condorcet winner (and I agree!) why not use a Condorcet method?
Woot! I've been asking that question for better than a decade.
It continues to be a curiosity that Center for Election Science likes to point to Burlington 2009 as an example of "broken RCV", but then they toss the baby out with the bathwater and impugn the ranked ballot when it's precisely because we have those ranked ballots that we know that the RCV election in Burlington failed in 2009.
If Approval Voting fails to elect the Condorcet winner, we would never know it (for sure). We might suspect it, but we would lack the ballot data to know for sure.
This is why I am simply a Condorcet guy.
The example you cite is one of my biggest complaints with IRV. If people are driven to vote dishonestly to compensate for a failure of the system, that tells me that the method is flawed.
It really is the seminal flaw. It is why, when IRV does not elect the CW, that IRV fails to deliver on literally all of its promises: guarantee electing the majority candidate when there are more than two candidates, eliminate the spoiler effect, remove the burden of tactical vote so that voters feel free to "vote their hopes not their fears" so that third-party and independent candidates have a level playing field with the two-party duopoly.
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r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
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