Later-no-harm criterion

The plurality vote, two-round system, instant-runoff voting, and descending solid coalitions satisfy the later-no-harm criterion. First-preference plurality satisfies later-no-harm trivially, by ignoring every preference after the first. Bloc voting, which allows a voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district, although the single non-transferable vote does. == Examples ==

Anti-plurality Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates. Later-No-Harm can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Harm can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below. Result: A is listed last on 2 ballots; B is listed last on 3 ballots; C is listed last on 3 ballots. A is listed last on the least ballots. A wins. ; Adding Later Preferences Now assume that the four voters supporting A (marked bold) add later preference C, as follows: Result: A is listed last on 2 ballots; B is listed last on 5 ballots; C is listed last on 1 ballot. C is listed last on the least ballots. C wins. A loses. ;Conclusion The four voters supporting A decrease the probability of A winning by adding later preference C to their ballot, changing A from the winner to a loser. Thus, Anti-plurality doesn't satisfy the Later-no-harm criterion when truncated ballots are considered to apportion the last place vote amongst unlisted candidates equally. Borda count ; Express later preferences Assume that all preferences are expressed on the ballots. The positions of the candidates and computation of the Borda points can be tabulated as follows: Result: B wins with 7 Borda points. ;Hide later preferences Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots: The positions of the candidates and computation of the Borda points can be tabulated as follows: Result: A wins with 6 Borda points. ;Conclusion By hiding their later preferences about B, the three voters could change their first preference A from loser to winner. Thus, the Borda count doesn't satisfy the Later-no-harm criterion. Copeland ;Express later preferences Assume that all preferences are expressed on the ballots. The results would be tabulated as follows: Result: B has two wins and no defeat, A has only one win and no defeat. Thus, B is elected Copeland winner. ;Hide later preferences Assume now, that the two voters supporting A (marked bold) would not express their later preferences on the ballots: The results would be tabulated as follows: Result: A has one win and no defeat, B has no win and no defeat. Thus, A is elected Copeland winner. ;Conclusion By hiding their later preferences, the two voters could change their first preference A from loser to winner. Thus, Copeland's method doesn't satisfy the Later-no-harm criterion. Schulze method ; Express later preferences Assume that all preferences are expressed on the ballots. The pairwise preferences would be tabulated as follows: Result: B is Condorcet winner and thus, the Schulze method will elect B. Hide later preferences Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots: The pairwise preferences would be tabulated as follows: Now, the strongest paths have to be identified, e.g. the path A > C > B is stronger than the direct path A > B (which is nullified, since it is a loss for A). Result: The full ranking is A > C > B. Thus, A is elected Schulze winner. ; Conclusion By hiding their later preferences about B and C, the three voters could change their first preference A from loser to winner. Thus, the Schulze method doesn't satisfy the Later-no-harm criterion. == Criticism ==

Douglas Woodall writes: ==See also==