Part 4: Voting Topics - Continued. Problems with Approval Voting Arrow’s Impossibility Theorem Condorcet’s Voting Paradox Condorcet. Problems with Approval Voting. Approval voting does not satisfy the Majority Criterion. the Condorcet Winner Criterion. the Pareto criterion.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Approval voting does not satisfy
Approval voting does not satisfy the majority criterion …
In this preference schedule, A has a majority of first place votes, however, by approval voting, the winner is B (with 4 approval votes, versus A who has only 3.)
Note: This example assumes that even though voters will vote only for the candidates they approve of, they can still rank those for which they approve.
To demonstrate another problem with approval voting, consider this example...
The Condorcet winner of this election would be A …
This is because 67 voters prefer A over B, and 66 voters prefer A over C.
That is, A beats the others one-on-one.
However, B is the winner of this election by approval voting. That is, the Condorcet winner was not elected and hence approval voting has been shown to violate the Condorcet Winner Criterion.
Again, the assumption is made that voters can still rank the candidates they approve of.
There is no voting method (nor will there ever be) that will satisfy a reasonable set of fairness criteria when there are three or more candidates and two or more voters.
In this preference schedule, even assuming
that individual preferences are transitive, it
becomes apparent that the group preferences
are not transitive…
For example, A is preferred over B by 2 to 1
B is preferred over C also by a vote of 2 to 1
and yet we see that C is preferred over A also
by a vote of 2 to 1.
Not having a winner is not a paradox by itself. In fact, there is no mention in Condorcet’s paradox as to what method of voting is being used, so no winner need be established. To repeat, what is paradoxical is this…
Suppose the group prefers A over B and prefers B over C. It would be expected, that the group would prefer A over C (that would mean the preferences are transitive.) But as can be seen from the table, C is preferred over A.