# Do "majority criterion" voting systems always result in "center-squeeze" effect?

1. In voting systems that meet the majority criterion, "if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win".

2. The "center-squeeze" effect is when a voting system excludes moderate candidates with broader, but less enthusiastic support, and elects more extreme candidates who have stronger support from a majority (plurality?), even if everyone else strongly disapproves of them.

It seems intuitively to me that these are the same thing, but is that correct? Does every voting system that meets the majority criterion necessarily also have the center-squeeze effect?

• The majority criterion is only true of multi vote systems, which are all pretty much designed to avoid problems of traditional voting like the center squeeze.
– user9389
Commented Dec 17, 2016 at 4:38
• I must admit I don't understand how this effect leads to extremists winning elections. Using the example the leftist can steal votes from the moderate by moving to the right so long as he doesn't move to the right of the moderate. Similarly the rightist can steal votes from the moderate by moving to the left so long as he doesn't move to the left of the moderate. So while the moderate would get squeezed out, he would get squeezed out by candidates that are as much like him as possible. Commented Dec 18, 2016 at 8:02
• @Readin Why would they move to be more moderate when they're already winning where they are? Commented Dec 18, 2016 at 16:32
• This question appears to assume a single-axis political division, as is common in the Westminster system. In multi-part democracies (i.e. not restricted to 1 or 2 parties) this is exceptional. Of course, the setup "if one candidate is preferred by >50%, that candidate must win" already assumes a single-winner election. Commented Dec 20, 2016 at 14:34
• @MSalters No, it happens in multi-dimensional spaces, too. "Squeezed Out" and "Disjoint" examples on Voting Simulation Visualizations rangevoting.org/IEVS/Pictures.html Commented Dec 20, 2016 at 14:52

Any voting system that is Condorcet compatible will comply with the majority criterion. I.e. the Condorcet criterion is strictly stronger than the majority criterion (as per your source). The Condorcet criterion also doesn't allow the center-squeeze issue. Let's take your example.

You note a system where 35% of voters prefer the left extreme (L) and 35% the right extreme (R). The remaining 30% prefer the compromise (C) as their first choice. Let's assume that those who prefer the compromise are evenly divided between left and right as their second choice. The compromise is the second choice for all those who prefer either extreme (and the other extreme is the third choice). And there are only the three options. In a Condorcet ranking, this would show as

• 35% L>C>R
• 35% R>C>L
• 15% C>L>R
• 15% C>R>L

So 35% prefer L to C (L>C>R) and 65% prefer C to L (R>C>L, C>L>R, C>R>L).
35% prefer R to C and 65% prefer C to R.
50% prefer L to R and 50% prefer R to L.

The net result is that C wins over both L and R on the first round (as the Condorcet winner). So in any Condorcet-compliant method, there is no center-squeeze.

The center-squeeze only occurs in a left/right paradigm like that when only the first choice voters are counted for the initial elimination. Examples of voting systems like that are Plurality and IRV (Instant Runoff Voting; also known as Alternative Vote and other names).

• Is there another criterion that does imply center-squeeze? Commented Dec 17, 2016 at 15:07