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A Smart Contract could be written to track a notional value greater than that of the value of ethereum contained in the contract, or even that of the stake of the miners in Proof of Stake, or the value of a bet implied by Proof Of Work.

For example there could be a contract that allows bets on off-blockchain gold futures, or some other off-blockchain measure of value, where the notional value of the bet is a significant fraction of outstanding ether on Ethereum, but doesn't actually use Ether to represent the value of the bet, but where the contract is merely used to irrefutably annotate the status of the bet.

If that notional value is a lot larger than the value of economic bet made by miners (in units of Ether), then it seems economically feasible to bribe miners to make the bet go in favor of the briber, e.g. by altering the contract's contents on a successfully bribed fork.

Is this actually a problem? If so, is the answer to this question "don't do that"? If that answer is "don't do that", then what's a good way to calculate the upper limit for notional value tracking on Ethereum?

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As far as I know, "don't do that" is indeed the best answer to this question. This is a problem, of course, common to every blockchain. It's always possible to bribe the miners or stakers if your economic clout is great enough.

Given the assumption of rational miners/stakers, a bribe would have to be greater than their future expected earnings. Doing this calculation can be somewhat tricky in a PoW system due to the significant role electricity costs play. In a PoS system, electricity costs are nowhere near as high and the cost of mining is entirely a function of how often a miner bets on the wrong chain (which is by definition a public value).

So the formula in a PoS system should look something like

bribe = (<avg staker success %> * <avg stake size> + <reward per block>) * (<number of stakers> * 0.51) * <avg expected length of staker participation>

This assumes a normal distribution of success rates and expected lengths of staker participation. Outliers could skew the number somewhat.

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    I've learned never to assume a normal distribution... – Paul S Apr 14 '16 at 20:52
  • Yeah. Normal distribution assumed just to simplify the example. Also because my math-fu is weak. – ryepdx Apr 15 '16 at 18:16

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