are weaker than the participation criterion are also incompatible with the Condorcet criterion. For example, weak positive involvement requires that adding a ballot in which candidate A is most-preferred does not change the winner away from A; similarly, weak negative involvement requires that adding a ballot in which A is least-preferred does not make A the winner if it was not the winner before. Both conditions are incompatible with the Condorcet criterion if one allows ballots to include ties. Another condition that is weaker than participation is half-way monotonicity, which requires that a voter cannot be better off by completely reversing their ballot. Again, half-way monotonicity is incompatible with the Condorcet criterion. Examples Copeland This example shows that Copeland's method violates the participation criterion. Assume four candidates A, B, C and D with 13 potential voters and the following preferences: The three voters with preferences A > B > C > D are unconfident whether to participate in the election. Voters not participating Assume the 3 voters would not show up at the polling place. The preferences of the remaining 10 voters would be: The results would be tabulated as follows: Result: A can defeat two of the three opponents, whereas no other candidate wins against more than one opponent. Thus, A is elected Copeland winner. Voters participating Now, consider the three unconfident voters decide to participate: The results would be tabulated as follows: Result: B is the Condorcet winner and thus, B is Copeland winner, too. Conclusion By participating in the election the three voters supporting A would change A from winner to loser. Their first preferences were not sufficient to change the one pairwise defeat A suffers without their support. But, their second preferences for B turned both defeats B would have suffered into wins and made B Condorcet winner and thus, overcoming A. Hence, Copeland fails the participation criterion. Instant-runoff voting This example shows that instant-runoff voting violates the participation criterion. Assume three candidates A, B and C and 15 potential voters, two of them (in blue) unconfident whether to vote. Voters not participating If they don't show up at the election the remaining voters would be: The following outcome results: Result: After A is eliminated first, B gets their votes and wins. Voters participating If they participate in the election, the preferences list is: The outcome changes as follows: Result: Now, B is eliminated first and