Economics and similar, for the sleep-deprived

A subtle change has been made to the comments links, so they no longer pop up. Does this in any way help with the problem about comments not appearing on permalinked posts, readers?

Update: seemingly not

Update: Oh yeah!

Friday, February 08, 2013

From my email outbox, on the importance of independence for left opposition

[this was sent during debates over US healthcare reform - "Dennis" is of course Dennis Kucinich, "Jane" is Jane Hamsher of Firedoglake]

The logic is only difficult if you assume that it always makes sense to give up in an ultimatum game, always makes sense to blink in a chicken-game and that the outcome of a voting process is always the median.  If you get even a little bit more sophisticated then it can make a lot of sense to oppose from the left.  I'll try and set it out in a totally deracinated and oversimplified model (note that I am not going to use any iterated results; I think people are correct to be very suspicious of "reputation", "credibility" and other results from iterated game theory).

First, set up a simple median voter model.  You've got a spectrum of possible healthcare reforms from 0 to 100, taking 0 as the rightmost and 100 as the leftmost position.  Say also that there are four groups in a unicameral parliament with 99 members and simple majority voting that are going to vote on it:

49 republicans, clustered at position 0
30 mainstream democrats, clustered at position 50
19 rightwing democrats, clustered at position 20
1 leftwing democrat called Dennis at position 100

The mainstream Democrats choose what bill to put before parliament and we assume that if it fails, this is equivalent to a bill of value 0 being passed.

Now let's take three alternatives

One, pure median voter with no strategic behaviour.  Everyone's (negative) utility is simply equal to  the difference between their ideal point and the outcome (if you are hung up on utilities being positive numbers, you can say that utility is equal to 100 minus the difference but frankly I think it's clearer to just work with negative numbers).

Outcome:  It is fairly obvious to see that the eventual outcome will be 39 - this has a value of -19 to right-dems which is better than -20, and for everyone to the left of them clearly any bill is better than 0.  This is the median voter theorem.

Two, Dennis's strategic model.  Make the additional assumption that for all Democrats except Dennis, there are political considerations which make the value of not passing a bill equal to -90 rather than 0.  For the right-dems, there is a 10 point political penalty for voting for any bill above 50.  Also assume that an outside party (called Jane) will give Dennis a psychic gift worth 98 if a bill pitched at less than 100 fails.

Outcome:  This is an equally uninteresting corner solution - there is one party who can make a credible threat and he gets what he wants. Dennis considers any bill at less than 99 as worth more to him dead than alive because of the present he gets from Jane. A bill at 99 is worth -89 to right-dems (79 for distance from their ideal point, plus 10 point penalty), but this is better than the -90 they would get from a total failure.  Since the mainstream Democrats need to make a coalition of themselves, the right-dems and Dennis in order to pass
the bill, they have to give him all the concessions.

Three, something closer to reality.  This is like model two, but the penalty for not passing a bill is X, an unknown number, and the value of the utility Dennis gets in the event of failure is Y, a number known only to Dennis and the unwillingness of the right-Dems to vote for a leftwing bill is Z, a number known only to them.

Outcome:  In order to pick their bill, the mainstream Dems need to make an estimate of X and Y, and then (on the assumption that these values are consistent with a bill being passed at all), choose the bill that combines the best chance of passing with the best outcome for them in terms of their ideal point of 50.  You can't say what will definitely happen, but you can be sure that the higher the Dems believe Y to be, the higher the number they will pick.  The relationship between X and the solution is complicated (because a bill
can fail because of either the right-dems or Dennis) and so is the relationship between Z and the solution, for the same reason.

Basically the point I'm making here is the one I made to Rich - if there is no possibility of left-wing opposition, then this just becomes a median voter game, in which the left will always lose.  If there is even a small likelihood of a nonzero Y, then it becomes a much more complicated game, but a game in which the eventual outcome gets monotonically better for them the more credible their threat is. In actual fact, Y is almost certainly a very small number compared to the difference between 0 and their preferred policy outcome, but clearly it makes sense to bluff that it might be a bigger number.


0 comments this item posted by the management 2/08/2013 04:57:00 AM

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