Hello All,
I'd like to get your opinions on this method, or actually a family of methods.
One short characterization (not an exact definition) of groupings is that instead of trying to identify clone sets or other groupings from the votes it could be better to let the groupings identify themselves themselves.
The used technique is that we don't have just one flat group of candidates but the group of candidates would consist of smaller groups. The groups may be hierarchical. For example instead of having a flat set of candidates {A, B, C, D, E, F, G} we could have groupings like {A, {B, C}, {{D, E}, F, G}}.
The meaning of the groupings is that candidates within a group (e.g. {D, E}) indicate that they are clones, belong to the same party or are just candidates that are friendly to each others. These groups are not strictly clone sets in the sense that voters would always position their candidates next to each others, but the basic idea of not causing harm to group members is the same. (It is possible to generalize the groupings to more generic alliances ((even unidirectional if you want)) where A would be a friend of B, and B would be a friend of C, but C would not be a friend of A. but for the purposes of this mail I'll stick to subset type alliances/groupings only.)
I'll jump to explaining how the votes might be calculated. You'll understand that better than any long verbal background explanations. I'll use minmax as the basic evaluation method and add groupings to that.
Voters vote just like in normal ranking based methods. Results are first counted just like in normal minmax with one exception. Defeats to other candidates in the same grouping are not taken into account when calculating the worst defeats of each candidate. Top level groupings are used in this first round to define which candidates belong to the same group (D, E, F and G are all part of one group in the first phase in the aforementioned example, others are A and {B, C}). It is possible that more than one candidate wins all her pairwise (non-friendly) comparisons.
In the second round only candidates that belong to the group that contains the winner of the first round will be considered. Let's say that the third group won. (In case of a tie the simplest thing to do is to flip a coin and decide the winning group right away.) In the second round subgroups within the winning group will provide protection to its members just like the top level groups did in the first round ({D, E} is the only group in the second round). All other candidates (also those outside the group that won the first round) will be taken into account when counting the worst defeats. The best subgroup of the first round winning group will continue to the third round (no such third level groups in our example). Rounds will end when the method picks a candidate that is not a member of any next layer subgroup.
Maybe this is enough to briefly describe the method. This method has some positive properties with respect to clones/parties/groupings/alliances and burying. Note that if the candidates are fully grouped (i.e. there are no groups with more than two members (groups or candidates)) there is no space for cycles of three. Already simple groupings (that have more than two members) eliminate the risk of losing because someone strategically creates a loop within the party.
If parties want to make sure that there are no loops they can arrange full grouping (at least within the party, not necessarily between parties). If there are no groupings, this is the basic minmax method that we used as a starting point. The method is thus to some extent flexible with respect to the anticipated level of burying threat (between or within parties).
One interesting additional possibility is that if there are many candidates and the groupings have names/numbers, then voters could name also groupings in the ballots. Someone could vote for example Kerry > Dean > Democrats > Bush > Republicans > Powell. Here group names would mean "any group members except those that are listed elsewhere in the ballot". Allowing style "Republicans > Powell" (one republican candidate listed after the party) is questionable for similar reasons why non-listed candidates are typically ranked below all listed candidates in normal ranking based elections - it is too easy to make unintentional mistakes and rank unnamed candidates too high.
The additional information that the groupings give to the voters may help the voters to make their decisions and see what the affiliation of each candidate is. (Or maybe someone would like to leave the definition of groups to voters in the spirit of "no parties in STV".)
My basic question thus is if you see groupings as a useful tool.
Best Regards, Juho
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