[EM] IRV vs Condorcet vs Range/Score

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> On Fri, 17 Oct 2008 22:08:32 +0200 Kristofer Munsterhjelm wrote:
>> Dave Ketchum wrote:
>>
>>> I suggest a two-step resolution:
>>>      Agree to a truce between Condorcet and Range, while they dispose 
>>> of IRV as being less capable than Condorcet.
>>>      Then go back to the war between Condorcet and Range.
>>
>>
>> I think the problem, or at least a part of it, is that if we (the 
>> election-methods members) were to advocate a method, to be effective, 
>> it would have to be the same method. Otherwise, we would "split the 
>> vote", as it were, against the status quo. Therefore, both Condorcet 
>> and Range groups would prefer their own method to "win".
>>
>> If that's true, then one way of uniting without running into that 
>> would be to show how IRV is bad, rather than how Condorcet or Range is 
>> better. If there's to be unity (or a truce) in that respect, those 
>> examples would focus on the properties where both Range and Condorcet, 
>> or for that matter, most methods, are better than IRV, such as in 
>> being monotonic, reversal symmetric, etc.
> 
> First, IRV will slay us all if we do not attend to it - it is getting USED.
> 
> Range and Condorcet are among the leaders and ask two different 
> conflicting thought processes and expressions of the voters:
>      Condorcet ranks per better vs worse, but asks not for detailed 
> thought:  A>B>C ranks A as best of these three.
>      Range easily rates A-100 and C-0.  Same thought as for Condorcet 
> would rate B between them, but deciding exactly where can be a headache.
>      Each of these has its backers, but we cannot devote full time to 
> this battle while we need to defend our turf against IRV.

Very true. While on one hand IRV gets people used to ranked ballots, 
it's a bad ranked method (IMHO), and when used with early-truncated 
ballot formats (like RCV), it doesn't even have the advantage of getting 
people used to ranked ballots.

> I suggest concentrating on Condorcet disposing of IRV because both use 
> almost identical rank ballots and usually agree as to winner.  They look 
> at different aspects:
>      Condorcet looks only at comparative ranking.  When they matter, we 
> ask only whether A>B or B>A is voted by more voters.
>      IRV cares only what candidate ranks first on a ballot, though it 
> looks at next remaining candidate after discarding first ranked as a loser.
>      Sample partial election:
>         9 A>E
>         9 B>A
>        18 C>A
>        20 D>A
>      A is WELL LIKED HERE and would win in Condorcet.  Count one last 
> voter for IRV:
>      A - B and C lose, and D loses to A.
>      B - A, E, and B lose, and C loses to D.
>      C or D - D wins.

Alright. So say that we (some of the members on this list) say to a 
hypothetical state (or the people there) that IRV is bad. Also assume 
they'll agree after having heard the arguments. Then they ask "What 
would you suggest?". I think the right answer, then, would be to say "If 
you're familiar with rank ballots, [Schulze, RP, pick best Condorcet 
method here]; if you want scored ballots, try Range", or something like 
that. Now, it may be that Condorcet is better (I think so), but again: 
defend against IRV.

That's a very quick example since it's obviously not going to be as easy 
as just "telling a state", but you get the general idea.

> What Condorcet calls cycles inspire much debate.  Optimum handling does 
> deserve thought, but could be directed more as to how to resolve them. 
> Real topic is that comparing rankings can show three or more of the best 
> candidates are close enough to ties to require extra analysis.
>      I claim this is a comparatively good thing - the worst candidates 
> end up outside the cycles and it is, at least, no worse than random 
> choice to award the win to what is seen as the best of them.

I think that when there's a cycle, the winner should be from the Smith 
set - that's just consistent with the idea of the Condorcet criterion. 
Once that's set, there would be two factors. The first is the simplicity 
of the method - a sort of "how 'electable' is this method?", though that 
would also include whether the method is in use elsewhere and so on. The 
second is the criteria the method satisfies.

Schulze has seen some use (mainly in open source communities, but also 
elsewhere), but it's hard to explain - perhaps the beatpath heuristic 
would be the best way. Ranked Pairs (by which I mean MAM) doesn't have 
the organization record Schulze has, but it's easier to explain 
("locking in", the explanation would probably start from showing that a 
one-on-one race is desirable, then that the method tries to reduce 
rankings to one-on-one races, one such race only beating another if it 
has greater strength).

Nanson or Baldwin could also work (they're basically Borda-IRV and thus 
extremely simple), but I think that would be too weak a compromise, 
since they aren't clone independent, and they're nonmonotonic (which 
could lead to the IRV supporters say "hey, weak centrist, still 
nonmonotonic which they yell about, IRV is clone independent and this 
isn't, and it doesn't even satisfy LNHarm/LNHelp!").

> Having election results in understandable format is valuable for many 
> purposes:
>      Condorcet records all that it cares about for any district, such as 
> precinct, in an N*N array.  These arrays can be summed for larger 
> districts such as county or state.  Also they can be published, in 
> hopefully understandable form, for all interested.
>      Range has less information to make available.
>      IRV talks of recounting ballots as it steps thru discarding losers 
> - at any rate not as convenient as Condorcet.

That's a good example of common advantages. Both Range and Condorcet 
(well, most of them; not Nanson/Baldwin) are summable. IRV isn't, and 
that may be important for logistics in large states. Besides (absent 
write-ins), the Condorcet matrices or Range totals (or {total, voters 
with opinion} for Warren's no-opinion version) could be published 
without having to deal with the fingerprinting vulnerability.

>> An expected response is that these properties don't matter because 
>> they happen so rarely. To reply to that, I can think of two 
>> strategies. The first would be to count failures in simulations close 
>> to how voters would be expected to act, perhaps with a reasoning of 
>> "we don't know what strategy would be like, but the results would be 
>> worse than for honesty, so these provide a lower bound". The second 
>> would be to point to real uses, like Australia's two-party domination 
>> with IRV, or Abd's argument that TTR states who switched to IRV have 
>> results much more consistent with Plurality than what used to be the 
>> case.
>>
> Condorcet has no interest in being like Plurality.  Its big plus over 
> Plurality is letting voters rank those candidates they want to rank as 
> best, etc., and using this data.

Of course. What I meant was that the "IRV is more likely to elect the 
plurality winner than is TTR" could serve as an argument against the 
adoption of IRV in states where TTR (top two runoff) is currently being 
used. If we're going to defend against IRV, then we should do so even if 
we can't get Condorcet (or Range) through, if the system to be replaced 
by IRV is better than IRV. Looking at properties, it seems like IRV 
dominates TTR (in the Pareto sense), but reality turns out differently 
(at least if Abd is right).

> Simulations are tricky - when can we honestly claim expected matches 
> reality?

They could give a rough order of magnitude idea of how prone certain 
methods are to failure of various sorts. But you're right here as well, 
you'd have to be very careful with the data and show it as such, not as 
the results of an oracle. It might also be useful to show to IRV 
supporters who think the monotonicity arguments are similar to arguments 
that favor Plurality to IRV - spurious reasoning with the real point of 
supporting the status quo. If the simulations show that monotonicity 
failure is common, then that would at least say "something is up", even 
if the simulations don't match reality very well.