Surpluses are treated differently from eliminated candidates in the election

Unfortunately we are not told how many of Bertie's votes were non transferable. Given the ultimate margin probably wouldn't matter what version of STV/PR was used.

We do see that out of Bertie's whopping (almost 1 quota) surplus Brady got 2,403 transfers and Paschal got 139, a ratio of over 17/1.
Similarly non-transferables were also transferred in the ratio 17-1 in favour of Brady. Now if someone voted for Bertie but did not transfer to his running mate is it reasonable that a similar ratio of 17-1 is applied? If you must preserve the total count then transfer the non-transferables in the ratio of first preferences, in this case 3.5/1 in favour of Paschal over Brady!! But if you really do wish to preserve the first preference count then spread non-transferable votes in an elimination in proportion to first preferences.
 
I don't think that is what he is saying. The rationale for transferring a surplus is that otherwise it has taken more than the quota of votes to get the candidate elected and so we deem that only a proportion of each vote that was needed and the remaining proportion is is still alive. So what proportion of you vote was used to elect A? The obvious answer is the quota/total number of votes credited. But under our system we differentiate between those who have further preferences and those who don't. The latter are deemed to have used all their vote to elect A, thus reducing the amount of the vote used up by those who did express a preference and thereby giving them a greater share of the surplus. The unfairness of this was well illustrated by the 2007 Dail election. The "celebrity" candidate, Bertie, swept through with 2 quotas. His running mate, Bradyonly got 30% of the first preferences of Paschal. Now as it happened if you simply voted for the celebrity but expressed no second preference, your share of the surplus was transferred to Brady vs Paschal in a ratio of 17/1 or in other words over 50 times their respective shares of first preferences.
Not sure I get this point. Yes the total count after distribution of a surplus is the same as the total count before. That is certainly not the case after an elimination unless you regard earlier "Non-transferable non effective" as part of the count (see second graphic in #123). One could of course maintain the count integrity after an elimination by gearing up the transferable votes. Then we would clearly see values greater than 1. The count integrity would be being maintained by making up for those that have fallen away by gearing up those that remain. The exact same process is taking place in our system on distribution of a surplus, albeit much more subtle. The folk who did not express a preference no longer have a say in the election but since the total count (say) has been maintained clearly those who remain have had an inflation of their vote.
Of course they are given a say on where the surplus goes. But it should only be to the extent that they own the surplus. If we regard non transferable surplus votes as orphans they should be farmed out in proportion to all first preferences and not the narrow constituency that agreed with your first preference,
 
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My terminology was a bit loose. These graphics indicate that there were no "Non-transferable non effective" votes in the first count. That is because if they had not indicated a preference they would be "forced" to be transferable by sharing them amongst the votes that did indicate a preference. This is where the "unfairness" in our system might arise and as I say we do not know the extent of that from these graphics.
In the Scottish system votes in a surplus that do not indicate a preference are regards as "Non-transferable non effective", consistent with eliminations.
In the Australian system ballot papers that are not completely filled are rejected so the issue does not arise.