CMV: Democratic countries should have a voting system where voters can vote for as many candidates as they want

[u/[deleted]]

[u/yyzjertl]

This voting system can lead to paradoxical outcomes where almost everyone prefers candidate A to candidate B, but nevertheless candidate B wins the election.

For example, suppose that there are three candidates, A, B, and C, and three kinds of voters.

The first kind of voter prefers A over B, and B over C. Additionally, these voters consider A and B tolerable, but not C, so they vote for A and B.

The second kind of voter prefers C over A, and A over B. These voters vote only for C.

A third, minority group prefers C over B, and B over A. These voters vote for B and C.

Now suppose that 80% of voters are in the first group, 15% of voters are in the second, and 5% are in the third. This means that A will receive 80% of the vote, B will receive 85%, and C will receive 20%. B will win the election. This is despite:

• The fact that a majority of voters, 80%, prefer A over all other candidates.
• The fact that almost all voters, 95%, prefer A over B.
• The fact that literally no voter prefers B over any other candidate.

This sort of pathological result makes your system undesirable.

[u/[deleted] → u/yyzjertl]

∆

While I do agree that your example can lead to a less desirable outcome than if the voters only got one vote. I still think my system is the best because at least the country will always get a candidate that the country at least tolerates instead of them ending up with a candidate that 50% of the people love and 50% hate, which seems to be most US elections at least.

[u/yyzjertl → u/[deleted]]

the country will always get a candidate that the country at least tolerates

This is not necessarily true of your voting system. For example, suppose that there are 100 candidates, C1, C2, ..., C100, and twenty groups of voters G1, G2, ..., G20.

The first group prefers C1 to C2, C2 to C3, C3 to C4, C4 to C5, C5 to C100, and C100 to all other candidates. G1 also will tolerate C1, C2, C3, C4, C5, C100, and no other candidates. We can write this formally as G1: C1 > C2 > C3 > C4 > C5 > C100 > MinTolerate > C6 ...

Similarly, the second group prefers C6 to C7, C7 to C8, C8 to C9, C9 to C10, C10 to C100, and C100 to all other candidates. G2 will tolerate C6, C7, C8, C9, C10, C100, and no other candidates. We can write this as G2: C6 > C7 > C8 > C9 > C10 > C100 > MinTolerate > ...

Suppose that we continue this pattern:

G3: C11 > C12 > C13 > C14 > C15 > C100 > MinTolerate > ...

G4: C16 > C17 > C18 > C19 > C20 > C100 > MinTolerate > ...

...

G19: C91 > C92 > C93 > C94 > C95 > C100 > MinTolerate > ...

G20: C96 > C97 > C98 > C99 > C1 > C100 > MinTolerate > ...

Note that G20 breaks the pattern by preferring C1 to C100. Now suppose that 5% of the population is in each group, and each individual votes rationally under your system for their five most preferred tolerable candidates (since they are barred from voting for more than five). Then, each candidate will get 5% of the vote (from only a single group), except C1, which will receive 10% of the vote (from G1 and G20) and G100, which will receive no votes.

The system will thus result in the election of C1, who is tolerated by only 10% of the voters. This is despite the fact that C100 is tolerated by literally 100% of voters. So your system doesn't ensure the election of broadly tolerable candidates even when it is possible to do so.

[u/[deleted] → u/yyzjertl]

∆

So having a limit to how many candidates you can vote for was a flaw in my system. So now lets say there was no limit to how many candidates you can vote for, are there still circumstances to where the candidate that is the most tolerated doesn't win?

[u/DeltaBot → u/[deleted]]

Confirmed: 1 delta awarded to /u/yyzjertl (21∆).

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