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Most election systems are "discrete" in the sense that each candidate is either elected or not elected. One could think of an election system that is "fractional", for example: if there are two candidates for presidency, one wins 60% and one wins 40% of the votes, then the first serves for 60% of the time and then rotates with the second, who serves for 40% of the time (to make it more practical, there may be a threshold of, say, 25%). It is similar to the idea of proportional representation, but applicable not only to parliaments but also to single-person offices such as presidency.

Is there a common term for such an election system?

I found the term "probabilistic social choice", which is somewhat similar, but the fractions are interpreted as probabilities, so in the above example, after the elections there is a lottery in which the first candidate is elected with probability 60%, otherwise the second is elected.

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    While rotating presidencies are not uncommon (e.g. European Council), I've never heard of one where the duration of the term is weighted.
    – Hulk
    Jul 15, 2021 at 10:19
  • (I realize though that this was just an exmple - I'm still trying to think of a voting system that might qualify)
    – Hulk
    Jul 15, 2021 at 10:37
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    I suppose systems where the winner gets to be the president, but the top n losers are automatically vice-presidents would not count for this question, because they don't really share power.
    – Hulk
    Jul 15, 2021 at 10:46
  • There have been rare situations in which the candidates in a disputed election agree to resolve a dispute this way, but there is no system that mandates it. The closest analog may be that in parliamentary system, different subject matters of decision making are often divided among majority coalition members.
    – ohwilleke ♦
    Jul 15, 2021 at 19:02
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    Maybe the closest is a system where the number of members of parliament is proportional to the vote total, as opposed to jurisdictions. Italy has something like that. In the 1980s, a political party in Italy got many more votes than they expected, resulting in several of their lowest priority candidates getting in, including a porn star who eventually offered to have sex with Saddam Hussein if he would get out of Kuwait.
    – puppetsock
    Jul 16, 2021 at 19:24

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It's impossible to prove a negative, but I will propose the answer is no, there is no such term and happily retract if someone finds one.

Consider the use case for such a system: The justification for these kinds of systems is that a candidate who gets n% of the vote deserves n% of the power. At a quick glance, 40% of the time of a given term may seem like 40% of the power associated with that office, but that's not actually how power works. 100% of the power, for 40% of the time, is still 100% of the power.

Political power is about the ability to say yes, no, and/or how much - rotating officers can't create the kind of tug-of-war that rewarding fractional portions of government power reflects.

So if you're going to try to build a system that grants power to voters based on their proportion of the turnout, you may as well just go for a proportional representation parliamentary system and be done with it. That's still not 'n% of the power' but it is far closer than trying to go King Solomon on a single office.

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    +1 Exactly. If a candidate wants to kill members of a minority and drop nuclear bombs on their neighbour, and won 1% of the vote, would you want them in charge of the country even for 1% of the time?
    – DJClayworth
    Jul 15, 2021 at 18:24
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    @DJClayworth - Clearly not, unless you're part of that 1%. :) A better question would be whether you think it would be fair to have them in charge for 1% of the time. And this is a good point even if there's a threshold (like the 25% suggested in the question). It's quite possible to do things in a small slice of time in power that can't be undone afterwards, regardless of how long the other candidate holds it. And if you put constraints on what they can do (or how fast), to the point where they can't get anything done in the time they have, what's the point of giving them time at all?
    – Bobson
    Jul 15, 2021 at 22:57
  • I agree that for state presidency the risk might be too high. But it may be a reasonable solution for some lower-stakes elections, for example, electing a chair for the neighborhood council or for a local club.
    – Erel Segal-Halevi
    Jul 16, 2021 at 8:32

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