[EM] Ranked ballots

[James Gilmour]

Forest wrote (in part, under "Recent postings"):
> My perspective on single winner methods has moved more and 
> more towards
> the point of view that ranked ballots are costly in terms of voter
> patience (as opposed to the cost of voting machines, ballot counting,
> etc.), and that the best Condorcet methods just barely 
> justify that cost
> in public elections, if at all, and that the other methods 
> based on ranked
> ballots fall far short of justifying that cost, though various ranked
> methods including Borda may have other applications in other venues.

These comments about ranked ballots prompt me to share some results from
an in-progress analysis of the ballots from one of the STV-PR elections
for the Irish Dail in 2002.  Ireland has used STV-PR to elect both
houses of its Parliament since 1920.  In 2002 all-electronic voting was
used in three constituencies (districts) and the full ballot "papers"
have been made available on the web.  So far I have looked at only one
of these datasets, for Meath.

There were 14 candidates for 5 places.  The two largest parties (FF and
FG) both put up 3 candidates. Four smaller parties each put up 1
candidate, and there were 4 non-party candidates.  There were 64,081
valid votes, so we have quite a robust dataset.  There is no restriction
of any kind on the number preferences a voter may mark.

The average number of preferences marked was 4.65.  Every candidate was
marked as every possible preference (1 - 14) by at least some voters.
The smallest group was 46 voters (0.07% of total) for one of the 14th
preferences.  The largest group was 11,534 (18% of total) for one of the
1st preferences.

Number		Percentage
of Prefs		   of
marked		Voters
   1		  5%	
   2		  7%
   3		33%
   4		19%
   5		13%
   6		  8%
   7		  4%
   8		  2%
   9		  1%
 10		  1%
 11		  1%
 12		  1%
 13		  1%
 14		  4%


There was an interesting difference in behaviour between the
'supporters' of the two parties that both put up 3 candidates.
(Supporter defined here as a voter who gave his or her first preference
to any one of that party's 3 candidates.)  Significantly more of FF's
supporters stopped at 3 preferences than did FG's supporters.  The
balance was made up at 5, 6 and 7 preferences, with a few more at 8, 9
and 10 preferences.

	Number
	of Prefs
	marked 	FF	FG
	  1	4%	3%
	  2	6%	5%
	  3	40%	28%
	  4	20%	20%
	  5	12%	16%
	  6	6%	10%
	  7	3%	5%
	  8	2%	3%
	  9	1%	2%
	10	1%	2%
	11	1%	1%
	12	1%	1%
	13	1%	1%
	14	3%	4%

Total number of Supporters:    FF = 28, 786    FG = 17,452
Between them these two parties gained 72% of the first preferences.

It is interesting to see in detail how real voters behave in real
elections.

Of course, the ballots for all the other STV-PR constituencies were
recorded on paper as usual and sorted and counted by hand, as they have
been at every election since 1920!
James