## What could be an appropriate electoral system, when some of the alternatives are similar to each other?

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Let us say people in a certain institution are given the choice to select one of four alternatives. While alternative 1 is to reject a certain policy, alternatives 2,3 and 4 are in favor of putting a certain policy into effect, with alternative 4 being the most extreme, alternative 3 the middle and alternative 2 the conservative way of implementing the policy. How could a fair and appropriate electoral system look like, if there can be only one ballot?

If everyone were given just one choice and the alternative with the highest number of votes were to win, chances are that alternative 1 would win and the policy would be rejected, even if the majority of people are in in favor of the policy, since votes will be divided among the three other alternatives.

If everyone were given the choice to rank all four policies according to his or her preferences and the alternative with the highest average rank were to win, it seems likely that alternatives 2,3 (the middle choices) would win.

How could an appropriate compromise look like?

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In general there is no fair electoral system when there are more than 2 choices. You have to sacrifice some criterion of fairness. https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem

– Matthew Liu – 2018-11-20T18:53:33.083

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The phenomenon you're describing is often called the spoiler effect, where similar candidates in a plurality based race end up impeding each other. One common measure of whether a voting system is susceptible to this effect is the "independence of clones criterion", where the winner doesn't change if another option is added which is identical (or very similar to) any of the existing ones.

In this case, it looks like you seek a voting system which is nearly as simple as basic plurality/first past the post (FPTP) voting, but which has this independence property. A popular choice is approval voting, which works on one ballot, with a virtually identical set of rules (one ballot, most votes wins) to FPTP, except without the condition that you can only pick one candidate. Instead, you put a cross in the box for every candidate which crosses your personal threshold of acceptability.

In theory, this maximizes the number of people who find the winning choice acceptable, while still being simple enough to explain in a couple of sentences (indeed, it's got fewer rules than FPTP). In practice, it's still possible that supporters of your alternative 1 would complain, because their preferred choice didn't win.

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Ranked choice/instant runoff voting could be useful here, although it is not perfectly ideal (and one could argue that no feasible election system can ever be truly ideal).

In a ranked choice system, the "yes" vote would avoid being split between three implementation options if many favoring "yes" would prefer one of the other implementations over a "no."

However this situation is very difficult to construct 'fairly'

Commenter @MatthewLiu mentioned Arrow's impossibility theorem which states that it is impossible to generate a ranked choice system that is fair by every relevant measure. I'll give one example of why this can be an issue:

If the balance between yes and no is similar and polarized, the "no" vote would get no influence in a ranked choice system (that is, if the vote is split 48% 11% 11% 30%, the most extreme option would be chosen if all of the alternative 2 and 3 voters prefer alternative 4 over alternative 1; the "second choice" of the alternative 1 voters, which might be a partial implementation is never considered).

The problem is further complicated by the fact that few policies can really be neatly divided into ranked alternatives. Informed voters could prefer either extreme of an issue rather than the center if they see problems with the "middle" option that aren't seen on either end, so any ballot that sets up a true ordered system and attempts to select a medium is already making a choice for the voters that the middle options are appropriate as compromises, even if none of the voters choose that middle option. For a silly example, imagine a ballot measure to legalize recreational marijuana, where an alternative is to only legalize recreational marijuana for households with an income greater than \$50,000. This is clearly a middle option between "legal for everyone" and "legal for no one," but I think many voters that would be either for or against legalization would be even more strongly against the "middle" option. Ranked choice could work fine in that situation, but some sort of median approach would not.

Other alternatives

Approval voting could also capture the yesses together but fail to discriminate between strong preferences between yes options.

There are various more complex systems that allow for voters to weight their preferences among possibilities, but these are also subject to problems including voter confusion and game theory issues that make it unclear how exactly a voter "should" distribute their preferences depending on their actual preferences.

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I think this is sufficiently answered by wikipedia's comparison of electoral systems. To summarize, there are 22 different game theoretical criteria that election systems are desired to have. The more criteria fulfilled, the better, although each criteria may not be equally important. There are 15 different majoritarian, single-winner electoral systems that are compared in this article. The electoral system with the highest raw number of criteria fulfilled is the ranked pairs method. Complications with implementing a different electoral system would be the same for ballot initiatives as for human candidates.

Like origimbo said, the independence of clones criterion is the criterion that is concerned with the interference of clones or spoilers. The electoral systems that are strongly immune to clones are instant-runoff voting, majority judgment, score voting, ranked pairs, Schulze method, and Random Ballot.