[EM] IRV in action

[Dave Ketchum]

On Sun, 30 Mar 2003 22:38:15 -0800 Rob Lanphier wrote:

> Very interesting.  It's a shame they didn't post the individual ballots 
> in a way that a Condorcet tally could be run.  I started to work out how 
> to reverse engineer the list based on the results, but unfortunately, 
> once a batch of ballots gets transferred from candidate A to candidate 
> B, it's impossible to know which ballots are which when candidate B's 
> ballots get transferred to candidates C, D, and E.
> 
> This looks like a really strange example of an election.  The 
> candidate/voter ratio was extremely high, and presumably, the candidates 
> had an opportunity to establish a somewhat personal relationship with 
> all of the voters (especially the incumbent pre-reform peers, who they 
> presumably worked with in the "good old days").  Thus, it's not hard to 
> imagine why the rankings were so deep compared with what you might 
> expect in another type of election.
> 
> It's also interesting how they chose to whittle down the number required 
> to win as ballots dropped off.  There were 423 ballots, where the first 
> column lists "Votes needed to be elected: 212".  However, by the time 
> you reach column 42, the votes needed to be elected drops to 134.  Is 
> this standard practice in IRV, or was this done to avoid the 
> embarrassing situation where no candidate in the runoff receives a 
> majority, even after receiving 42 rounds of ballot transfers?
> I suppose this is an interesting problem for IRV in general.  I'd always 
> been under the impression that a big selling point of IRV is that the 
> winner would have "a majority", even if it's from a series of 
> transfers.  However, there's no guarantee that there will be a majority 
> even after all of the transferring is done.  In this particular 
> election, there's no knowing how many of the 115 ballots accumulated by 
> Montgomery of Alamein (the runner up) in the 42nd round actually listed 
> Ullswater (the winner) next (who won with 151 votes).  If less than 61 
> ballots (i.e. 212 minus 151) of the 115 Montgomery of Alamein ballots 
> had listed Ullswater, then there was indeed no majority winner.


Here you need to understand the language IRV uses - they LIKE the word 
"majority", treading lightly on the fact that they are doing a majority of 
the ballots that remain to be used to determine a winner, and not a 
majority of total ballots.

BTW - "majority" is a word that often needs qualification, such as "most 
of those who voted" or "most of the members".

With dozens of candidates (required to give 42 rounds something to work 
on), no voter should be required to rank every candidate, for it is 
unreasonable for voters to be expected to intelligently rank so many.

Now, assuming A and B are liked better than the many Ms, and that some 
voters consider A and B to be less acceptable than any of the Ms they are 
prepared to rank, there will be ballots that are exhausted before we get 
to A vs B.  So the "majority" will simply be based on comparing A vs B, 
and be more than half of the ballots that included one or both of them in 
a voter's ranking.

Oops, what I wrote above is not exactly right, but I choose to keep it in 
and correct it here:  Certainly ballots do get exhausted, so the majority 
to win is likely less than half the total ballots - it just has to be more 
than half the non-exhausted ballots.  So, if A has such a majority, then B 
and the remaining Ms, together, must have less, meaning that whatever 
might happen to the remaining Ms, A will still have a majority - and 
therefore the election can be terminated at this point without determining 
how decisively A won over B.

There was interest above as to whether some Montgomery votes might have 
listed Ullswater as a lower choice.  I see no value in this as these 
voters voted against Ullswater by listing Montgomery first.

True IRV weakness that I see:
      44 candidates got some first place votes and can, possibly, win - 
          even with two to get started with (candidates with only one 
could list them next).
      Some of the above may have got only one - here the IRV counters 
decide which of these die now and which, if any, get a chance to advance.
      37 got no first place votes.  These all die instantly, even if one 
of them got 400 second place votes - this happens because, whenever some 
of their second place votes get exposed, those will be discarded as lowest 
count among the remaining votes.

> 
> Rob
> 
> James Gilmour wrote:
> 
>> For an example of a real IRV election see
>> http://www.parliament.uk/
>> and select the link for Hereditary Peers By-Election.
>> It is a PDF file (27 KB) so you may want to "Save target as ..".
>>
>> There were 81 candidates, of whom 44 received one or more first 
>> preference votes.
>> There were 423 valid votes.  The count went through 42 stages, right 
>> to the wire
>> for the decision between the last two.  Interestingly, there were no
>> non-transferable papers until the 18th stage and the number of 
>> non-transferable
>> papers did not rise significantly until stage 40.
>>
>> Ullswater, the IRV winner, received the greatest number of first 
>> preference votes:
>> 86 (20%).  So he would have been the FPTP winner.  But the runner-up 
>> did not
>> receive the second greatest number of first preferences - he was third 
>> and didn't
>> pick up any transfers until the 25th stage.
>>
>> James

-- 
  davek at clarityconnect.com    http://www.clarityconnect.com/webpages3/davek
   Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
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