This is an electoral system based on Condorcet with Approval Voting. Condorcet with Approval Voting asks voters to rank candidates in order of preference and to indicate which candidates the voter finds to be acceptable. When no circular preference exists in the electorate, meaning that there is a candidate who would beat every other candidate in a two-way race, it is possible for a different candidate to be an acceptable choice to more people than that Condorcet Winner. The candidate acceptable to the most voters is called the "Approval Winner." When the Condorcet Winner and the Approval Winner are different candidates, CVA compares the percent of the electorate preferring the Condorcet Winner over the Approval Winner to the Approval Winner's overall approval rating and chooses whichever is higher.
Examples
The following examples show how percentages of the electorate might vote in a hypothetical election between four candidates, A, B, C, and D.
  • 60% rank them ABCD and approve A and B.
  • 15% rank them CABD and approve only C.
  • 15% rank them CABD and approve A, B, and C.
  • 10% rank them BACD and approve only B.
Notice that A is the Condorcet Winner since A is preferred over B by 90%, over C by 70%, and over D by 100%. Therefore. CAV would choose A as the winner, while the Approval Winner would be B with 85% approval, since A's approval is 75%, C's is 30%, and D's is 0%. In this case, Condorcet Versus Approval would produce the same result as Condorcet With Approval because 90% is greater than 85%. Here's another example in which the two methods choose different winners:
  • 60% rank them ABCD and approve A and B.
  • 15% rank them CBAD and approve only C.
  • 15% rank them CABD and approve A, B, and C.
  • 10% rank them BACD and approve only B.
The difference from the previous example is in bold. Now, A's preference over B has been reduced by 15%, to 75%. Since 75% is less than B's approval rating of 85%, CVA will choose B. The winner of the election has been changed because of the preferences of C's supporters. This is counter-intuitive at first because so many people (75%!) prefer A over B. However, if we follow that logic to an extreme case where the "so many people" is just barely a majority, it will become more intuitive:
  • 51% rank them ABCD and approve A and B.
  • 15% rank them CBAD and approve B and C.
  • 15% rank them CBAD and approve B, and C (and not A).
  • 19% rank them BACD and approve only B.
Now, just over half the people like A better than B, but everyone approves of B and it seems obvious that B should win to avoid the tyranny of the majority. It may now seem that perhaps Approval Voting is the better system, since in the examples in which it is clear which candidate should win, that candidate is the Approval Winner. So let's look at a final example in which most would agree the Approval Winner is not the best choice:
  • 46% rank them ABCD and approve A and B.
  • 5% rank them BACD and approve only B.
  • 34% rank them CABD and approve only C.
  • 15% rank them CDAB and approve only C.
In this case, A is the Condorcet Winner by 95% over the approval winner, B, who is acceptable to 51% while A is acceptable to only 49%. To ignore the preferences of 49% of the electorate (C's supporters who all liked A better than B) just to get a candidate who is acceptable to 2% more of the electorate seems unreasonable.

Thus, we have cases where the Condorcet Winner should win, and cases where the Approval Winner should win. When you start looking at the voters who make up the difference that CVA uses, you see that it enables the "losing voters" to cooperate in avoiding a solution that completely ignores them. Whether this cooperation is based on who they find acceptable or based on which winning candidate they prefer depends on which of these two areas achieves the greatest consensus.

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