The Irish 1990 presidential election, won by Mary Robinson

"Success" or "failure" for Instant Runoff Voting (IRV)?

by Warren D. Smith, Sept. 2007.    (Conclusions 1 2 3 4 have pink background.)

1990 Presidential Election - 7th November 1990
Electorate: 2,471,303 Turnout: 64.10% Total #Voters: 1,584,095 Quota: 787,326
Candidate Party 1st Preference % Transfer of
Currie's vote
% Final
Mary Robinson Labour 612,265 38.89 +205,565 76.73 817,830 52.79 wins
Brian Lenihan Fianna Fail 694,484 44.10 +36,789 13.73 731,273 47.21
Austin Currie Fine Gael 267,902 17.01 –267,902 -------
Non-transferable votes   25,548 9.54
Totals 1,574,651 100.00 1,549,103 100.00

This election is often cited by IRV proponents as an example of a great success for IRV. But let us examine it. It turns out that despite the very-partial report above from the Irish Election authority, we still can discern pathologies.

"Participation failure" pathology (& also "favorite-betrayal" failure)

Suppose we magically added a new "Currie County" to Ireland comprising 344,364 new identical voters, each voting Currie>Robinson>Lenihan. [This is fairly realistic, since Currie-top voters did in fact prefer Robinson over Lenihan by a 6:1 ratio; the Currie votes split (77%, 14%, 9%) for (R, L, untransferable).]

Then Robinson would have been eliminated in round 1.

Let us assume that the Robinson votes would have transferred

(≤52, ≥39, 9)% to (Currie, Lenihan, untransferable),
or let us merely assume that those numbers were only (upper, lower, equal) bounds, respectively, as I've indicated with the "≤" and "≥" signs. This also is realistic.

Irish politics interlude [from Irishman Ivan Ryan]:
Lenihan was the subject of a controversy, so it is reasonable to assume that his support was substantially party based (core FF voters are probably in the region of 35-40%... perhaps less so now). An FF-core voter would likely vote against an FG candidate. The flip side of this was seen when the FG candidate (Currie) was eliminated; 77% voted 2nd choice against FF.

However, FG/Labour have closer ties than FF/Labour as FG has no hope of forming a government without Labour. FF on the other hand has a realistic chance of forming a government with the support of either smaller parties (or Labour). So there probably would be at least a 2-1 split in FG second-place votes in favour of Robinson. [End of Ryan quote]

Finally, Lenihan was considerably more popular than Currie as we see from both the vote and a poll in the 10 October Irish Times indicating FF-over-FG support by about 49% to 24%. Hence the majority of Robinson's 2nd-preference votes probably would have gone to Lenihan.

So this (≤52, ≥39, 9) assumption seems quite plausibly realistic. It is actually probable Lenihan would get considerably more than 39% of Robinson transfers, so our assumption seems quite comfortably satisfied.

OK. Under this assumption, the first round totals

Currie  612266         would have become after         Currie ≤930644
Lenihan 694484         the Robinson-transfers          Lenihan≥933267 (wins)

Conclusion: In this case the new Currie voters would have made a big mistake by voting honestly, since their Lenihan-last votes would have made the hated Lenihan win. They would have been better off "staying home" and not voting (as, in fact, they did) or better off "betraying" their favorite Currie and voting Robinson top instead (as, in fact, considerable numbers of them perhaps did). This election thus had (what voting theorists call) a "no-show paradox."

Monotonicity failure and/or Favorite-betrayal failure

Consider the 694,484 Lenihan voters. Some voted Lenihan>Robinson>Currie; others voted Lenihan>Currie>Robinson. Suppose that 344,364 (i.e. 49.6%) of them had voted the latter way.

Warning: This is not a very realistic assumption. As we said, most FF voters would be inclined against FG, so assuming this many Lenihan voters chose FG second, is unlikely. Nevertheless, let us explore the consequences of this assumption, then only later re-examine the assumption itself.

Then those 344,364 voters would have been foolish to have thus-voted honestly since (as the official election results show) that caused the hated Robinson to win. If they had instead strategically betrayed their favorite Lenihan to instead vote Currie top, then

  1. Lenihan would have been eliminated in round 1 whereupon
  2. Currie would have won, which these voters would have preferred.
  3. Indeed – assuming (now entirely realistically) that the Robinson voters would have 2nd-choiced Lenihan more often than Currie – then (in a situation just like this but featuring enough extra Currie voters so that fewer Lenihan voters had to be dishonest) their favorite Lenihan would have won!

So this election is an example of favorite-betrayal failure: under our assumption about the composition of Lenihan voters, the act of honestly voting for their favorite (Lenihan) was a stupid mistake that caused their most-hated candidate (Robinson) to win. Smarter was to dishonestly vote Currie.

But it gets crazier, as we hinted at above in point (3). The altered-version of this election with 612264 Currie voters (the extras added from "Currie County") would have been an example of monotonicity-failure:

Conclusion: These 344,364 Lenihan voters actually made Lenihan+Currie lose by voting for them and would have made Currie win [which they preferred over what happened] by strategically voting against Lenihan. Further, in the altered-election with extra (in total 612264 due to 344362 from a "new County") Currie voters (which Lenihan still wins), if anywhere between 2 and 82221 Lenihan voters (in percentage terms 0-12% of them) then chose to vote strategically for Currie instead of Lenihan, that actually would have made Lenihan win!!

Re-examination: Note in the altered election it doesn't matter whether our 49.6%-assumption was unrealistic. The fact is, whether or not it was valid, 12% of Lenihan's supporters still could have made Lenihan win by instead voting for Currie. They would have been strategically stupid to all vote for Lenihan. That's just a fact.

What kind of pathology was that last one, anyhow?

It seems clearest to regard this election as suffering from a hybrid form of the "non-monotonicity" (type-II) and "no-show" paradoxes. Specifically, if

(a) 344362 new "Currie>Robinson>Lenihan" voters had appeared and
(b) 2-to-82221 Lenihan-top voters had switched to Currie-top
   (the non-top parts of their votes don't matter, so we can if we want make them switch from "Lenihan>Currie>Robinson" to "Currie>Robinson>Lenihan"),
leaving everything else unchanged, that would have made Lenihan win.

The (a) part is the no-show component of the paradox, and the (b) part is the non-monotonicity.

We therefore are certain that either this election yielded the wrong winner (Robinson) or that the thus-modified election would have yielded the wrong winner (Lenihan) or both.


In the whole of (central govt, i.e. not counting lower level such as county and town, elections) Irish history so far (up to 2007) there has only been a single IRV election in which the winner differed from the plain-plurality winner, i.e. in which the Irish use of IRV vote-transfers actually directly mattered.

This (1990) was it. (And actually, Irish mayors are not directly elected and nor are county heads, so it may be that the President is the only IRV-elected post in the country at any level of government, in which case this is the only IRV election where IRV made a difference in all of Irish history.)

In this single example of Irish IRV success, the election exhibited several pathologies. Lenihan could quite justifiably have complained (if he had realized this!) that he deserved to win:

  1. If a whole new county had magically appeared with 344364 new voters, all of them supporting my most-hated rival and ranking me in last place... then I would have won!
  2. If (in addition to having that new county now packed with just 344362 Currie supporters) 12% of my supporters had switched their vote to my most-hated rival Currie while ranking me last – then I would have won! (Although: without my supporters switching over to Currie in this way, I would have lost?!?!)
  3. So why the heck didn't I win?

Mind you, we aren't complaining that Robinson won. That worked out well for Ireland. We are complaining that IRV malfunctioned, or at least, that its legitimacy was dubious in this case. If approval or range voting had been used, there would have been no such dubiousness; we believe Robinson would have clearly won (or perhaps Lenihan?), and definitely, none of these three pathologies are even possible with approval and range.

January 2008: I thank Phil McKenna for pointing out an error in an earlier version of this page. It has now, hopefully, been corrected.

Analogous look at Australia's 2007 election cycle

Puzzle 55d: the presumed underlying theoretical reason this pathology is so common

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