We here answer some questions about our detailed DH3 analysis. To summarize, I contend that the DH3 scenario is an extremely common and extremely serious problem afflicting Borda and every (meaning: wv or margins) Condorcet voting method.
A. Not really. There is no Condorcet cycle (with roughly 50-50 mixtures indicated by the commas) in the honest votes – C is the honest Condorcet winner:
| #voters | Their Vote |
|---|---|
| 37 | C>A,B>D |
| 32 | A>B,C>D |
| 31 | B>A,C>D |
...and there is no Condorcet cycle in the scenario with everybody (or most) voting strategically either (the "dark horse" D is now the Condorcet winner):
| #voters | Their Vote |
|---|---|
| 37 | C>D>A,B |
| 32 | A>D>B,C |
| 31 | B>D>A,C |
But we admit some thinking about cycles was involved, in a sense, in the decision by the A- and B-voters to use this strategy (which was intended to create a cycle to prevent C from winning and thus cause A or B to win). However, we contend many A- and B-voters would have done that even without ever having heard of Condorcet cycles, since it is a natural attempt to most-hurt their candidates' perceived major rivals.
Check this evidence
that real human Australian ranked-ballot voters
use this sort of "maximal exaggeration" strategy in massive numbers.
Indeed,
the Australian parties themselves advocate this kind of voting strategy.
Also, it is known from poll data
that about 90% of Nader-favorite voters voted, strategically,
for somebody else in
USA 2000.
I was asked: "why would voters act in this strategic manner if they know it risks the DH3 pathology
of electing D?"
Well, voters have to assess their risks and benefits. If they raise D, they are more likely to
elect their favorite, but also more likely to trigger the pathology and elect D.
So a voter might say "ok, I will be altruistic and vote honestly, thus not risking electing D."
Trouble is, then the voters on the other side, who are not altruistic, can afford to
play the D-raising game and will succeed in their strategic goal! The situation is very
similar to the game of "chicken."
That isn't a good game for a voting system to resemble.
The critic's question more fully was: To make a dire warning about how "DH3 pathology" could cause "massive destruction" if any of the voting methods that are theoretically susceptible to it are used is little more than a rhetorical ploy... What is most lacking in this and other discussions about strategic voting is empirical data about how people vote in actual public elections in which different voting methods are used... If the point is to make arguments that are logically compelling, such rhetoric is not merely unhelpful but extremely counterproductive.
A. The reason I consider DH3 to be extremely serious and destructive (as opposed to some non-serious random election pathology example) is that it is extremely common and when it happens it is very bad. It is the combination of the two.
I think these are objective criteria, not inflamed rhetoric. (And see above about real-life data from Australian elections.)
The question more fully continues: This situation could arise if the candidates ABC are the vertices of an equilateral triangle, D is its center, and all voters are located near A, B, or C and voters prefer candidates closer to them.
A. Yes, in this scenario, each voter honestly would rank D second and D would then be the honest Condorcet winner. Also, D might then be the honest range voting winner (depends how highly the honest voters score D) or that might be one of {A,B,C}.
In this situation the C-voters in Condorcet would be strategically motivated to downgrade D in their votes to bottom (below all others). If enough voters did that, then D would no longer be Condorcet winner and one of {A,B,C} would win. (For concreteness, say C would win.) Of course, in that case some voters (i.e. the A- and B-voters) would then want to upgrade D... with the result
| #voters | Their Vote |
|---|---|
| 37 | C>D=A=B |
| 32 | A=D>B=C |
| 31 | B=D>A=C |
so D would (fortunately for all) win despite this strategizing and restrategizing (and with either margins or winning votes Condorcet).
Meanwhile with range voting, the C-voters also would strategically want to vote C=99, B=A=D=0 and if enough voters acted that way one of {A,B,C} would win (say C for concreteness); but then the voters for the losers (A and B) would be motivated to upgrade D to co-equal top with 99, and then D would win. So in this situation, range voting and Condorcet voting both (after strategizing) yield the same winner D, who as the question-poser stipulated, is the honest Condorcet winner.
So if the intent of the questioner here was to devise a counter-scenario in which Condorcet looks good and Range Voting looks bad, that attempt failed.
The questioner had originally asked why the A- and B-voters could not agree to just all vote for A. The answer to that was "because then B would have zero winning chances, so the B-party and B-voters wouldn't go for that deal." He then asked this. This agreement would work, except in reality, usually what will happen is, it will not be (and cannot be) clear to the voters who is collaborating with whom to defeat whom.
E.g, suppose all the voters know is: there are 3 strong rivals A,B,C and a dark horse D. They do not have precise-enough estimates on who has how many votes exactly.
In that case (the questioner conceded) "I agree. Without a clear frontrunner to try to defeat, I don't see how you could hope for even an incidental alliance with another faction."
The short answer is "no."
My questioner continued: [The CRV] talks of the "DH3 pathology" as a serious problem that should encourage Condorcet backers, such as myself, to abandon ship and switch to IRV.
The questioner then went on to point out, e.g, this situation which makes IRV look bad and Condorcet look good:
| #voters | Their simplified vote | Their full (implied) vote |
|---|---|---|
| 30 | A | A > B = C = D |
| 25 | C > B | C > B > A = D |
| 23 | D > B | D > B > A = C |
| 22 | B | B > A = C = D |
In this example, B is the easy Condorcet winner but IRV elects A; the latter seems obviously silly since the voters prefer B over A by 70-to-30.
A. The questioner misinterpreted the goal of our "salesmanship." It happens to be true that IRV is better than Condorcet in the DH3 particular kind of situation. However, Condorcet seems better than IRV in other situations, including Ketchum's example election above. For more examples: Schulze beatpaths Condorcet is monotonic, never suffers from a winner=loser reversal-pathology, and always elects Condorcet winners if they exist; but IRV enjoys none of those properties.
The correct moral to draw is that IRV and Condorcet both suffer from serious problems and the simpler range voting system, which tends not to suffer those problems, is better. In particular: