As an instrumental rationalist, I would say that 0 is a better approximation than 1/2 ....

How is this train of thought "instrumental"? You aren't making any choices or decisions outside of your own brain.

To make it a real instrumental example, consider whether or not you should go buy a meteorite shield. Lets say the shield costs S and if the meteorite hits you it costs M, and the true probability of the strike is p. So buying the shield is best if pM > S.

Now if you go with 0, you'll never buy the shield, so if pM > S you have an expected loss of (pM - S) due to your approxamation.

If you go with 1/2 then you'll buy the shield if M/2 > S. If M/2 > S and pM <= S then you bought the shield when you shouldn't have, and you lose and expected (S - pM).

So you see, it all depends on how big M is compared to S

M < S/p : 0 is the better instrumental approximation

M > S/p : 1/2 is better

In other words, if the risks (or payoffs) are small compared to the probabilities involved and the costs of shields, round to 0. Otherwise round to 1/2.