# Is there an election system in which the outcome is fractional?

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.

• 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
• 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. Jul 15, 2021 at 19:02
• 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. Jul 16, 2021 at 19:24