[EM] Bucklin-Condorcet PR

[Chris Benham]

Previously, in the "Condorcet elimination PR" thread, I wrote:
"Further  on the subject of my proposal  to modify STV-PR by , after 
transfering supluses, eliminating the Condorcet loser among those votes 
and fractions of votes not tied up in quotas: I am afraid I have 
discovered that this method fails FBC (Favourite Betrayal Criterion).
To demonstrate the problem, I have slightly modified your example by 
introducing  candidate X.

300 votes,  3 seats,  Droop quota = 75.

74   A B C D X E
39   B A C D X E
75   C
37   D X E C B A
73   E D X C B A
 2   X E D C B A

Compared to your example, all that has changed is that X has  stood and 
taken  2 first preference votes from D and has occupied  the runner-up 
Condorcet loser position. The result, CBD, is unchanged.
The problem is that if  those 2  X  supporters had reversed their top 
two preferences, then E would have got a quota and the result would have 
been CEB. By insincerely down-ranking their favourite, those two voters 
could have caused their second prefernce to be elected instead of their 
third."
This was maybe not so clever because this is just the mildest form of 
FBC  which no ranked-ballot method can avoid. For a simple single-winner 
example, I lifted this from  http://www.condorcet.org

45 ABC
35 BCA
25 CAB

"In this example, A would normally win. However, the BCA voters could 
improve the outcome (from their perspective) by voting CBA, which would 
result in C winning with a majority of first place votes."
With sincere voting, A is the clear beats-all CW (as well as the 
Plurality and IRV winner), but by "betraying" their favourite, the B 
voters can elect their second preference C.

I now propose a non-elimination version of ranked-ballot PR, which 
combines Bucklin and Condorcet.
Ranked ballots, equal preferences ok. Count the first preference votes. 
Equal  preferences are divided into equal fractions (which sum to 1).If 
any candidates have  a Droop quota they are elected, and then reduce the 
values of the ballots which have elected members by an amount which sums 
to a Droop quota.
If more than one place remains unfilled,  proceed to to the second 
round. Add the second preference votes to the first preferences (based 
on the value of the ballots after the any reductions that were  made the 
previous round). If this gives any candidate a Droop quota, then elect 
the candidate with the highest tally. If  there is a tie, then elect the 
tied candidate who had  the bigger tally at the last round, if still 
tied then the round before that if  there was one, otherwise the 
Condorcet winner of the tied candidates based on the ballots after the 
most recent devaluations. Reduce the value of the ballots that  elected 
this winner by an amount that sums to a Droop quota. If  there is still 
more than one place unfilled and if after the latest devaluing of 
ballots any candidates have a Droop quota, then elect the one with the 
highest tally (same tie-breaking proceedure) and so on.
If there is more than one place to be filled, then add the third 
preference votes to the tallies of first and second preferences and if 
that gives any candidate a Droop quota, then as before the candidate 
with the highest tally is elected and so on.
If  proceeding in this way leads to the situation where there is one and 
only one more place to be filled, then based on the ballots after all 
the devaluations elect the Condorcet Winner.

This method is I think simpler to count than any version of STV, and it 
might be monotonic.It performs very well in all the examples that I have 
seen that showed up Condorcet Loser elimination STV. In the simple 
example at the top, it elects C A E in that order.
Soon I will post more on this, going through some examples.

Chris Benham

















-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20030807/7210e5eb/attachment-0002.htm>