(Epistemic Status: Superficial application of complex topic to complex domain)

In a representative democracy, there is always a tension between the need for elites to make unpopular decisions and the need for elites to be held responsible for mistakes by the public. In the US, the contrasting term periods of the Senate, House of Representatives, and Supreme Court reflect different choices on this spectrum of accountability and trust. Unfortunately, there is a substantial flaw in this method, namely that decision-makers respond mainly to their remaining time in the office (before the next election, etc.) rather than their total time for the period. We can see this in how politicians tend to focus more on legislation earlier in their term and focus more on winning elections near the end. As a result, a term length of (for example) 5 years has the incentives of a 5-year term for some of the time, the incentives of a 4-year term for some of the time, the incentives of a 3-year term, and so on.

This is not great since, ideally, you would want to pick a single set of incentives for an office holder to act under that correctly balances the tradeoff. Luckily, it is possible to do exactly that, it just requires a bit of randomness.

A forgetting solution

The trick is to use a memoryless process like a Geometric or Poisson Distribution. In a memoryless process, the future distribution remains the same after each time step. For example, if you are flipping a coin until the first heads, it doesn’t matter how many times you’ve already flipped it, the distribution over future flips is the same. We can use this same property in the context of term lengths to keep the incentives of an office holder exactly the same over time, i.e. have the expected time remaining always be equal to some optimal period. For example, you could flip a weighted coin near the end of every year (maybe a month in advance) for whether a particular office will be up for election and then set the weighting to have an expected term of 5 years.

This is especially good because for any incentive-optimal expected time, you can pick the right probability and time-step length for your geometric distribution and then you’re done!

Obviously, this is not a super realistic solution to the political issues mentioned at the start, but systems like this are pretty useful for many compliance/inspection problems so I think it’s worth considering how they might generalize.