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Luke_A_Somers comments on Imperfect Voting Systems - Less Wrong
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In many Condorcet systems, you don't need to provide a total ordering - you can have ties. In those systems and IRV, you can use a truncated ballot - any name not on the list is ranked at the bottom.
I don't have anything against Approval - I think it's a fine system, and easier to build hardware for - but I don't think ranking systems are all that problematic.
I think you underestimate how difficult it is to create a voting system that won't utterly baffle a large portion of the electorate. People in general aren't good about reading instructions, and they often get confused about the simplest of things. While I like both Condorcet and approval voting, I prefer approval voting for being stupidly simple. "Vote for the people you think would do a good job; the person with the most votes wins," is a very easy thing to understand, so most people will probably get it.
(Think I'm being too cynical? Try writing non-trivial instructions aimed at ordinary people. You'll see.)
What about a bubble-fill, with multiple bubbles per candidate? Instructions, beyond the standard how-to-darken-a-bubble stuff, amount to "fill in more bubbles for the candidate(s) you really like, fewer bubbles for the candidate(s) you don't like so much, and no bubbles for the candidate(s) you don't like at all." Maybe some examples. Vote-reader filters out the noise of exactly which bubbles were filled, then normalizes each ballot into a preference ranking, plus some implied trivia about preference strength.