Example to demonstrate why IRV cannot be counted in precincts

(Demonstration that IRV is not "additive")

Counting votes in precincts (or counties), then sending the precinct totals to the statewide election office – it has been a way of life in almost all US states for as long as any of us have lived.

But if we were to switch to IRV (instant runoff) voting, that would no longer be possible. All the votes, en masse, would have to be given to statewide central tabulating for them to count; there simply could no longer be such a thing as a "county subtotal."

Is that an insuperable obstacle to adopting IRV voting? No. It'd be a huge change in US election procedures, financing, and organization, and it might make everything much more easily vulnerable to huge centrally-organized election frauds – you won't be able to observe your and your neighbors' own votes being counted anymore – but it won't be fatal to IRV, since central counting is certainly possible.

To make it clearer why there is no such thing as a district "subtotal" anymore if we use IRV voting, consider the following example.

District I: B wins
#voters Their Vote
6 A
4 B
3 C>B>A
District II: B wins
#voters Their Vote
6 C
4 B
3 A>B>C

In district I, IRV eliminates C, then B wins 7:6. In district II (same as district I but the roles of A and C are reversed), B also wins 7:6. But in the combined 2-district country, B has 8 top-rank votes, A and C have 9 each, so B is eliminated and either A or C wins. Thus merging two districts both won by Bush under IRV, can produce an IRV victory for Gore.

Wait – Can't IRV be counted in precincts (and on old-style plurality machines) in this other way?

IRV can be done on plurality machines, and counted in precincts, by simply making each permutation (rank ordering) be a "candidate."

Our response: That's true but practically infeasible. In a C-candidate race, each voting machine would have to have C! pseudo-candidates and each precinct would have to pass C! "subtotal" counts on to the central tabulator. If C is large this is infeasible:

C 3 4 5 6 7 8 9 10 11 12 13 14 15
C! 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000

(Aside: Actually, it is even worse than this if voters are allowed to "truncate" their preferences – then even more than C! ballot types become possible, namely ⌊C!e⌋ where e=2.71828… and note, if you do not count an all-blank ballot as a "ballot type," then subtract one. See puzzle #91.)

Note, 13! is about equal to the present world population. Heck, you could just pass all the V votes to the central tabulator, and that'd be easier than passing the subtotals (if C!>V) which defeats the purpose of having subtotals. (A typical precinct has V=2000 voters. But 7! = 5040. Also if the IRV rules allow "ballot truncation" then the true number of ballot types actually would be much larger than C!.)

So "counting in precincts" is silly if precincts have to pass an exponentially large amount of information along – larger than just not totalling at all and just sending all the votes in unprocessed form!

Also, more to the point, I want precinct totals to be published. That's not going to happen if a precinct is going to have to publish 6!=720 "totals" in one race. And even if that did happen, then this publishing would defeat ballot secrecy and open the door to vote-selling and coercion.

Wait – Can't IRV be counted in precincts via Two-Way Communication?

Yes. IRV can be counted in precincts if there is two-way communication between precincts and headquarters – headquarters informs all precincts who to eliminate next, then precincts report their top-rank totals (among remaining candidates) and then the cycle repeats.

But this basically is centralized counting. If you have counting in one central location directed by some "director," what is the difference versus having it in, say, ten central locations, directed by that same director using modern two-way communication technology?

So yes, it will still work. And according to Rob Richie (June 2008 web post), "In Ireland there are 43 counting centers in the presidential race. Election administrators count ballots and report their totals to a national office that in turn instructs the administrators at each counting center on what to do next. The entire process takes less than a day even though more than a million ballots are cast."

There are several problems with the rosy picture Richie here tries to paint. First, doing this requires modern communication technology, e.g. computer networks. (E.g. Richie suggests "If ballot images are recorded on optical scan equipment, the data from those images can be collected centrally.") It won't work if that communication technology is disabled, broken, misused, or attacked. That's a step backwards (increased vulnerability, reduced simplicity, reduced transparency) versus voting systems like plurality and approval where precinct subtotals exist and no two-way communication is needed.

Second, this is a centrally-directed scheme. There still is no such thing as a "district subtotal." If a district counts its ballots locally under central direction, then it cannot publish its subtotals because there is no such thing as a district subtotal. That reduces the transparency and checkability of elections.

And doing this could require all workers at every location to keep counting and recounting until every single last vote everywhere gets counted, which'd be a very long workday (or perhaps a better word than "day" is "month"...).

The problem is if central doesn't know whom to eliminate next because that depends on a very close vote which depends on every last absentee ballot, missing chad, debate over who intended what on some unclearly-marked ballot, etc. And even if this particular elimination-decision might between two "no hopers" who have only 1% of the vote each, each elimination decision can amplify arbitrarily much and thus alter the ultimate winner, so Central can't just "ignore the issue and move on." And then everybody everywhere has to remain at work waiting a month for Central's next announcement. And in principle such a chad-counting nightmare could happen in every IRV round. So the worst case scenario is really very bad.

If indeed, every precinct in the USA (I think there are over 100,000 of them) were to try to count ballots under central direction as Richie has in mind, that could require every precinct-worker in the entire USA to keep counting for 1 month. That would raise the cost of elections astronomically. So in fact (to avoid that) really the counting would need to happen at a much higher level than "precinct," such as "statewide." Which is fine – but then it is not local anymore and it is a big change from today's organization of elections with local, not central, counting.

The way many IRV countries actually do it is, they do a single pass making a probabilistic model of who is likely to be eliminated and in what order. If the model turns out to be correct, then everything goes smoothly. If it turns out to be wrong, then they get into trouble and have to start recalling the election workers and doing more counts... If it gets it wrong in more than one way we can really get into huge difficulties... but fortunately this in practice seems rare, probably because all IRV countries so far have been 2-party dominated. In Australia's 24 November 2007 elections, the Election Commission was unable to determine the composition of parliament until over 1 month later because of numerous races which were difficult for them to count.

Here's what happened when North Carolina tried to do IRV with precinct counting...

The enormously complicated official rules (pdf) boggled everybody's mind.

We thank Kathy Dopp for contributing this info about North Carolina. (She also wrote a paper summarizing 18 flaws in IRV.) She concludes: "It will be nothing short of a praise the Lord miracle if this process is performed accurately in all polling locations." Note that even after adopting this hugely-complex procedure, North Carolina still failed in the sense that if some IRV decision made before its final round (for example, its first round) were a close one, then even this procedure quite likely would not work – the IRV counts would have to be restarted from the beginning and counted centrally. Even early-round subcontests between candidates who might naively seem to have no hope of election, can have ballooning effects which alter the ultimate winner.

Analogous problem for Condorcet voting systems

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