You are partially correct, in that you are on the right track about how the algorithm works. It might happen that somebody does something like that, sure, although that particular kind of ballot is actually a horrible idea. I examine a more reasonable strategy that is similar in concept in the PDF under Preliminary Analysis. But first of all, it doesn’t actually become plurality unless there are only two candidates remaining anyway, since candidates are eliminated in turn, not chosen as winners. Second of all, by doing that sort of thing, their top choice candidate is not likely to win the whole election at all. In fact, based on their own ballot, their candidate is very likely to be eliminated in the first or second round.

Each round eliminates a candidate, and if all of a voter’s candidates are eliminated, their string is empty and no longer counts. So they are being exceedingly risky—splitting their own vote, engaging in a risky anti-plurality elimination, wagering on which candidate is likely to be eliminated early and even counterbalancing that prediction with their own ballot. Additionally, if it were a reasonable strategy, you would expect many people to do something like that, but the strategy requires having a rare ballot because otherwise the whole strategy destroys its own precondition of knowing which candidate is likely to be eliminated.

For example, let’s say there were 3 candidates, A, B, and C. Let’s just do a small electorate with like five people. Say the votes are like

ABBBBBBBBB

AAAAAAAAAB

CCCCCCCCCC

CCCCCCCCCB

BBBBBBBBBA

Well, now A is eliminated the first round. The counted characters in the next round then look like

B

B

C

C

B

then C is eliminated, and B wins, contrary to the preference of the first voter.

Now let’s say that voter is instead more reasonable, and votes like AAAAAAAAAB. Then we will find

AAAAAAAAAB

AAAAAAAAAB

CCCCCCCCCC

CCCCCCCCCB

BBBBBBBBBA

Now B is eliminated first, and then C, and A wins.

Do you see how that works? Let me make an example where B does get eliminated first:

ABBBBBBBBB

AAAAAAAAAA

CCCCCCCCCC

CCCCCCCCCB

AAAAAABBBB

Well now, when it comes to plurality, there are only two candidates anyway, and A is a reasonable winner for the election. But the first voter would have given A an even better chance of victory with a string like AAAAAAAABB or something. Instead he has basically contributed to his own vote-splitting and made it more likely for C to win over A. For example, the votes could have instead been like

ABBBBBBBBB

AAAAAAAAAA

CCCCCCCCCC

CCCCCCCCCB

CCCCCCBBBB

And A gets eliminated in the first round again. Another example to illustrate the more reasonable strategy:

AAAAAAAAAB

AAAAAAAAAA

CCCCCCCCCC

CCCCCCCCCB

CCCCCCBBBB

Now B is eliminated the first round instead of A. A still doesn’t win the election, but you can see that A was carried further. Making it to round 1 is a prerequisite to round 2, and round 2 is a prerequisite to victory.

You can try out your own little simulations with this, they aren’t too difficult to do by hand with small electorates.

Perhaps four candidates are necessary to illustrate why that strategy doesn’t work well. I’ll work on that a bit more when I’m somewhat less busy.

OK. Say we have A,B,C,D. Let the votes be like

ABBBBBBBBB

AAAAAAABBC

BBBBBCBCCA

DDDDDDDDDC

CCCCCCCAAB

CCCCCCAAAB

In this case, D is eliminated first, and we find

A

A

B

C

C

C

Now B is eliminated, and we find

A

A

C

C

C

C

And C wins. Now let the first voter be more reasonable:

AAAAAAAAAB

AAAAAAABBC

BBBBBCBCCA

DDDDDDDDDC

CCCCCCCAAB

CCCCCCAAAB

D is still the first eliminated. And we find

A

A

B

C

C

C

Now B is eliminated, and we find

A

A

C

C

C

C

The end result was the same in this case. We can see about this one:

BBBBBBBBBA

AAAAAAABBC

BBBBBCBCCA

DDDDDDDDDC

CCCCCCCAAB

CCCCCCAAAB

It becomes

B

A

B

C

C

C

Now A is eliminated, and it becomes

BBBBBBBBB

BBC

BBBBBCBCC

C

CCCCCCCB

CCCCCCB

A tiebreaker is needed. C: 3+4+1=8, B: 1+4+4=9. So B wins the election in this case.

But let’s see what happens if many people try that strategy. Let’s say B and C are small potatoes, and A and D are big party guys. Trying to force the election to turn into a plurality, the voters indicate their major party and then a “throwaway” candidate as you suggest. Some of them vote as I imagine is reasonable:

ABBBBBBBBB

DCCCCCCCCC

ABBBBBBBBB

ABBBBBBBBB

DCCCCCCCCC

BBBBBBBBBA

CCCCCCBBBA

DDDDDDDDDC

Let’s see what happens. A is off the bat eliminated:

BBBBBBBBB

DCCCCCCCCC

BBBBBBBBB

BBBBBBBBB

DCCCCCCCCC

BBBBBBBBB

CCCCCCBBB

DDDDDDDDDC

Now D is eliminated.

BBBBBBBBB

CCCCCCCCC

BBBBBBBBB

BBBBBBBBB

CCCCCCCCC

BBBBBBBBB

CCCCCCBBB

C

And B wins the tiebreaker. So actually, even the threat of that tactic gives supporters of third parties more incentive to indicate the third party candidate as their top choice, since “pluralists” will shower them with votes for the sake of…something.