[EM] Groupings, alliances, friendly relationships

[Juho Laatu]

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