[EM] Situations where IIA failure may be natural

[Kristofer Munsterhjelm]

IIA failure is generally considered to be a bad thing. But perhaps 
sometimes "all things equal" is not so!

Consider the restaurant joke: Sidney is offered a choice of apple pie 
and blueberry, and says "I'll have apple". Then the waitress says "Oh, 
we also have cherry". "Well, in that case, I'll take blueberry". This 
seems completely unreasonable.

But here's a variant. Suppose I'm a fan of desserts that are difficult 
to make, like (just picking something here) baked Alaska and meringue 
pie. But I know that they're easy to get wrong and so I'll settle with 
apple pie as a good dessert that's easy to make.

I'm visiting a restaurant with generally good reviews and I ask what 
desserts they have. They say "there's meringue pie and apple pie". I'm 
not willing to risk, despite their good reviews, that they can pull off 
the meringue properly, so I say "okay, I'll have apple pie". Then the 
waiter says "Oh, hang on, we also have baked Alaska".

Now I may reason: given the good reviews, and that they have multiple 
difficult desserts, more people may have tried the difficult ones; so if 
they weren't any good, it wouldn't have been reviewed so well. So I say 
"well, in that case, I'll take the meringue".

In a political context, the closest thing would be something like: I've 
moved to a new town, and there are local elections with some left and 
right parties. The parties' candidates seem sensible at first glance, 
but they could just be tailoring their message to the audience. Now if 
I'm a left-wing voter (say), and there are multiple left-wing parties, 
this may indicate that there's a demand for left-of-center policies, and 
thus that the left-wing candidates are more likely to mean what they're 
saying, thus making it less risky to support one of them.

It's kind of tenuous, but still I thought it's an interesting example :-)

If it's at least somewhat realistic, it could bring more subtle dynamics 
into elections, no matter whether they pass IIA or not. For instance, if 
voters are likely to consider a particular political position more 
sincere if there are multiple parties based on it, then that's an 
obvious (theoretical) clone failure. On the other hand, maybe not so 
much: the inference works precisely because it's hard to set up proxy 
parties that seem legitimate. If that becomes easy, then there's little 
value in the observation, and the voters would stop judging the number 
of parties as an indication of the strength of the position.

-km