This 100-voter example election illustrates an old controversy between Borda and Condorcet dating back to the days of the French Revolution in the 1700s. According to Condorcet, A should win. (A also wins under the IRV voting method.) But according to Borda, B should win. Who really should win? Good question.
Now let's see how range voting would handle this. If the voters say
|51||A=99, B=70, C=60|
|49||B=95, C=90, A=85|
|Average||A=92.14, B=82.25, C=74.70|
then A wins. But if they say
|51||A=99, B=95, C=40|
|49||B=90, C=85, A=40|
|Average||A=70.09, B=92.55, C=62.05|
then B is the winner.
The point is that range voting allows voters to say how much they prefer B over A (or whoever). Quantitatively. Really, Borda or Condorcet are both right – but who is right depends on intensity-of-preference information that simply is unavailable to their voting methods, but is available to range voting. So this example illustrates an advantage of range voting over both of these previous voting systems.
Here's a pictorial example and another cleaner version (we don't need no stinking numbers, we want a Picture!)
Another example is in puzzle 30. In that example, Borda and Approval voting both are clueless but range voting, thanks to quantitative preference information in votes, can act sensibly. And here is yet another example that makes the same point perhaps even more powerfully.
Still more examples (by Professor Stephen Unger, Columbia University, NY) this time demonstrating how approval voting can also have more expressive power than any ranked method.
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