You're finishing up a nice dinner, when the waiter lets you know about their dessert options. They have apple pie (A), and blueberry pie (B). You order a nice hot slice of all-American apple pie. A minute or two goes by, and the waiter returns. "I forgot," he says, "to mention that we also have cherry pie" (C). You consider it a moment and decide, "In that case, I'll have the blueberry."
Just Dessert
Ridiculous, isn't it? If you think A is the best out of A and B, then there's no logical reason you would think that B is the best out of A, B, and C. But what if pies are parties, and you are the American voting public? Official results don't collect voter's full preferences on candidates, but (please, hold off on your Gore/Nader (or Bush/Perot) comments for a bit, thank you!) there's no shortage of people claiming that this new third option, even though they didn't win, changed the outcome. (Keep holding it.) What we're talking about is usually called the spoiler effect, or more broadly and academically, a failure of the independence of irrelevant alternatives (IIA).
In the absence of 100%-completely-non-controversial data, it's easy enough to construct a plausible example to showcase the theory:
- 30%: A > (all others)
- 45%: B > (all others)
- 25%: C > A > B
This isn't C's fault. Maybe C was making a statement. Maybe A should have dropped out of the race. Maybe C's voters valued their honest vote over the practicality of supporting a "lesser evil." (Okay, now you may comment.) All of these could be true, or none of them could be true, but the fault lies not in our candidates or our voters, but in the way we have agreed to count our elections. We have decided to use a voting system which fails the independence of irrelevant alternatives. And IIA means spoilers, which means "the lesser of two evils" is an effective voter strategy, which means we will have a two-party system. In other word, not only will C lose, but C will always be feared by voters of potentially causing the election of the worst candidate.
Declare Your Independence
This is not a new revelation; this is a problem we've been aware of, and trying to fix, for at least a few hundred years. But, in 1951, Kenneth Arrow proved--on his way to a Nobel prize--that no (single-winner) voting system can pass IIA if it is both deterministic and based on ranked-order ballots. That leaves us with precisely three options.
- One, accept failure of IIA (which means we accept our two-party system.)
- Two, allow a random component in our elections (not a popular plan.)
- Three, don't use ranked-order ballots.
Declare your independence from irrelevant alternatives! Support approval voting and other third-party supporting voting systems.
Or you can mitigate the problem by enhancing IRV w. the use of Approval Voting in the first stage and trust that there are also ways to subvert the use of deceptive clones in real life.
ReplyDeletethus, the hazard from the IIA pathology may not be that high and so choice A becomes to make our two-party system meritocratic or a "two major parties at a time" system.
dlw
Sure, you can always mitigate.
ReplyDeleteBut you cannot ELIMINATE spoilers (AKA, IIA failure) with any deterministic rank-based voting method. And as long as spoilers exist, the tendency toward two-party domination is very, very strong. Mostly, I think, because human beings are risk-averse, making the lesser of two evils very, very tempting.
The only IRV elections that get spoiled are ones where the two biggest parties fail to center themselves around the true center, as occurred w. Burlington. This capacity to spoil gives strong incentive for the biggest parties to adapt or die, which is what would have happened if IRV had survived the smear campaign run by the defenders of the status quo. It seems to me that there's a hell of a diff between making third party-dissenters vote strategically for a major party and making members of a major party that refuses to adapt to vote strategically. IRV does the latter, only. In a multi-period game, it's worth it for a successful third party to keep on growing so as to move the de facto center to the true center.
ReplyDeleteAnd, just because our current 2-party system is so dysfunctional does not imply that 2-party domination is the root cause of problems in our system (a correlation is not a causation). If we also soften up the tendency to 2-party domination via the strategic use of PR in "more local" elections that o.w. tend to be rarely competitive, we could end up with a very different sort of 2-party system.
My vision is a contested, meritocratic duopoly with an indefinite number of minor parties and a large number of LTPs that take advantage of the diseconomies of scale in forming community to rely principally on volunteer power so as to effectively check the influence of $peech on the major/minor parties. The collective influence of such a two-party system would be more like a melding than a melting pot!
dlw
That's not correct at all though. Centrism doesn't guarantee victory under IRV.
ReplyDeleteConsider a slightly different version of the "1-d politics" game from this post. Place a party directly in the center. Now, if I can place two more parties, I can always make your centrist lose. ALWAYS. And you can't move more-centrally to do anything about it (I can actually make it so that you can still win by moving AWAY from the center; how's that for perverse incentives!)
Now, this doesn't work with a Condorcet method, or a Borda method, or if you use honest range votes, or even approval (with multiple variations on what approval thresholds voters use); if you play in the very center, there's nothing anyone can do that makes you lose under any of those methods. You can see this playing with Ka-Ping Yee's Voteline tool.
In this way, plurality and IRV are UNIQUELY capable of losing this game for a centrist candidate. And things only get worse for IRV (and all other systems, but especially IRV) when you move to models more-complex than 1-d spectrum.
Fair point about correlation and causation though; Duverger's "Law" is really just an observation, not a proof. However, I'm reminded of the paper you pointed out to me last June, which used a candidate entry/exit model that suggested that approval would better-encourage centrist candidates to enter races; even though the "real race" was still a choice between just two candidates (which was the point you wanted to harp over, that "approval doesn't resolve two-party dominance"), their research showed that the POSITION those two candidates would be in, unlike with ranked methods (including IRV) would be two NEARER to the center, because approval rewards (i.e., increases the expected value for) candidates towards the center, because they don't act as spoilers. And I think that's fascinating... and now I'm reminded that I wanted to post about that.
Another alternate game:
ReplyDeletePlace two candidates anywhere you want (as long as they're between two voters.)
I can always change the winner with a third party.
I won't necessarily be a spoiler, because sometimes I will be the winner, but when I am the winner, I will also be less-centrist than your original winning candidate.
Check that: I won't always be more centrist; if you pick two extremist (both either <25 or >75), I can win by being more-centrist. If you pick one centrist (between 25 and 75) and one extremist, I can win by being less-centrist than your centrist. If you pick two centrists, I can change the winner by being an extremist.
ReplyDeleteAgain, none of this is true for non-plurality non-irv methods.
Good to spar again, Dale.
ReplyDelete"Place a party directly in the center. Now, if I can place two more parties, I can always make your centrist lose. ALWAYS. And you can't move more-centrally to do anything about it (I can actually make it so that you can still win by moving AWAY from the center; how's that for perverse incentives!)"
dlw: Ah, but in this example, the two biggest parties are in fact close to the center(as I predicted)... and so the fact that the most centrist party doesn't win is relatively small potatoes.
And as for the 3rd party candidate winning by going way from the center, that's a curiosity due to the uniform dist'n of voter preferences. That isn't realistic...
I've played with Yee's voteline thingy. The issue is with the uncertainty as to what is the center, since it's something that's dynamic.
That's why I downplay the import of "center squeeze". The center can't be cordoned off by anyone and so to pick a rule based on how it pins down the center is like chasing after the wind.
With both IRV and FPP, there's pressure to move twds the center by the biggest parties, it's stronger with IRV. Thus, the de facto center ends up becoming more closely tied to the true center.
Let's say a shift in voter preferences has D and R at the 70 and 71 penny marks and G sets up shop at 35. G wd win with both FPP and IRV, but both D and R get to move again. But there are rigidities that prevent them from moving too much too fast. And so the D's move to 55 and the R's to 56. And then G still wins if it's FPP, but with IRV then R wins.
But what if D moves and R (perhaps stuck in FPP thinking) doesn't move, so the positions are 35, 55 and 70? In that case, G would win.
Tragedy, right? But it can be expected that the next election will change things further so that the G's must move to the right(or merge w. the Ds) and the R must move to the L or merge with the Ds.
The moral of the story is that parties are like the people groping around in the dark in Socrates' cave. They cannot choose exactly where on the spectrum they will be. But IRV helps us to adjust and makes the outcome closer to the center than o.w. with FPP.
If Approval Voting had been used then D would have won by moving to 64. In fact all the parties wd be strongly encouraged to beeline for whatever the center seemed to be and with a shifting center, they'd all stumble and bump together in the dark.
Whereas, the Gs by taking a stand at 35 at least they succeed in moving things to the left or maybe they'll get lucky...
It's not an exact science, which is what it should be. We want people to pursue the center, but not too doggedly...
Sorry if that's fuzzy, but I think that's closer to real life...
dlw
If you've got your two major parties at 25 and 75, 75 can win by moving toward the center, sure. But then they lose if another party--or more likely, another candidate from the same party--stays at 75.
ReplyDeleteThat's the same effect that primaries have with FPTP (with the right assumptions about voter partisanship, IRV works precisely like party-primaries-plus-FPTP.) I've got to say, you are simply incorrect about IRV having any centerward pull. (And then of course there's even more madness when there are more than 3 choices.)
Meanwhile, under Condorcet, Borda, approval, and range, with this simple model, the winner is always the candidate closest to the center (even when you add a 4th, 5th, or more candidates!) And that means there's an incentive for a party to move its policies toward the center under just about ANY election method... except FPTP and IRV
But Dale, you're not making your model very realistically...
ReplyDelete"If you've got your two major parties at 25 and 75, 75 can win by moving toward the center, sure. But then they lose if another party--or more likely, another candidate from the same party--stays at 75."
dlw: Aye, but it's not easy to build up a party base where one can become a player. There are barriers to entry and there's intra-party discipline that wd prevent a spoiler within the party from helping the other party's candidate to more likely win... If anything such a threat wd keep the candidate from moving all the way to the center, which doesn't contradict my point that IRV rewards major parties that move twds the center and spoils major parties that refuse to do so...
DHS: That's the same effect that primaries have with FPTP (with the right assumptions about voter partisanship, IRV works precisely like party-primaries-plus-FPTP.)
dlw: I'd like to hear more about that sometime....
dsh: I've got to say, you are simply incorrect about IRV having any centerward pull.
dlw: "Any" pull? That's a very strong conclusion, based on a highly contrived counterfactual!
As an engineer, you need to follow the dialectic between theory and empiricism more closely. You're relying too much on theory.
In my view, there needs to be more realism in view of voters habits and the party's limited ability to enter a race and relocate or to even pinpoint the true political center. O.W., the theoretical results are pretty wild and far from empirical observation, especially with more than two parties.
DSH: Meanwhile, under Condorcet, Borda, approval, and range, with this simple model, the winner is always the candidate closest to the center (even when you add a 4th, 5th, or more candidates!) And that means there's an incentive for a party to move its policies toward the center under just about ANY election method... except FPTP and IRV
dlw: Aye, but not every hypothetical election that can be dreamt up is useful for evaluating election rules and we can't even presume that nailing the true center a lot is the summum bonum for us if there's a fickleness in how multiple political dimensions get collapsed into a single-dimension political spectrum over time....
There's a need for both change and continuity in politics, since all major changes take time.