Sunday, May 21, 2017

Bad Deal Or No Deal

Consider these two statements:
  • Eating no bread is better than eating any mouldy bread.
  • Any bread at least as good to eat as no bread is not mouldy.


To avoid ambiguity, let’s put them into Mickey Mouse first order logic:
  • (x)[[Mouldy(x) & Bread(x)] → Better(eatingNoBread,eating(x))]
  • (x)[[Bread(x) & ¬Better(eatingNoBread,eating(x))] → ¬Mouldy(x)]


The two formulations are equivalent: they are both false iff there is some mouldy bread the eating of which is no worse than eating nothing. But there’s a difference of emphasis. The first formulation is something you might say if you were taking an uncompromising line on bread: if mouldy bead is all there is, you’d rather have nothing. The second formulation is something you might say if you were taking a compromising line on mouldiness: it can’t be mouldy or you wouldn’t recommend eating it at all. But a difference in emphasis is not a difference in commitment. Asserting either commits you to the same things.


Now, the government’s line on the Brexit negotiations is apparently that no deal is better than a bad deal. People take this as meaning that they’re taking an uncompromising line on deals, and they take it to embody an attitude of cavalier intransigence. But consider these two statements:
  • Reaching no deal is better than reaching any bad deal.
  • Any deal at least as good as no deal is not bad.


And in MMFOL:
  • (x)[[Bad(x) & Deal(x)] → Better(reachingNoDeal,reaching(x))]
  • (x)[[Deal(x) & ¬Better(reachingNoDeal,reaching(x))] → ¬Bad(x)]


The second formulation seems to embody an attitude of roundheaded compromise. Don’t criticize this underwhelming deal, they say, because it’s better than nothing. But the two formulations are formulations of the same commitment. In the mouldy bread case the speaker enjoys a certain amount of latitude because of whatever vagueness and subjectivity there is in the word “mouldy”. In the Brexit case the speaker enjoys latitude because of whatever vagueness and subjectivity there is in the word “bad”.


Now with the mouldy bread case, the speaker is at least committing themselves to something. That’s because some bread is determinately mouldy. Suppose the only food available is determinately mouldy bread, and you say that eating no bread is better than eating any mouldy bread. Half the party eats the bread, against your advice, and half the party goes hungry. One half has a better time and you are open to praise or criticism as a result.


Now consider the Brexit case. While we don’t have a whole party to divide up into people taking your advice and people not taking it, we can still compare the actual world with our dimly assigned probability distributions over the space of counterfactual situations. But the government can always evade criticism, whatever consensus history arrives at on the relative merits of no deal and the available deals. Obviously the government are also the people taking the decision, unless they lose the election, and so they could be open to criticism for taking one option if history judges that other available options would have turned out better. There’s no escaping that. But the particular claim that no deal is worse than a bad deal is entirely hedged.


Take any deal you like. If we decide that it’s worse than no deal, the government says it’s bad and takes the credit for being right. If we decide that it’s better than no deal, the government can just say that it wasn’t a bad deal. Similarly, nobody needs to praise the government however things turn out either. If history judges that the available deal was worse than no deal, the opponent can say that of course there are some deals worse than no deal, but there are plenty of bad deals better than no deal too, and if we’d been able to get one of those then the government would have turned it down and been wrong to do so. The word ‘bad’ and the associated concept are flexible enough that nobody ever needs to admit they were wrong about whether no deal is worse than a bad deal. The government shouldn’t be criticized for taking a bad line; they should be criticized for empty, commitment-free rhetoric.

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