Typically, does it seem that voters are unflinchingly concerned about only the prospects of just one single candidate? As true as that probably is when there are only two candidates, more generally a voter is apt to find several that seem acceptable and several others to seem completely unacceptable. Despite such a likely possibility, plurality voting insists that the voter pick only one to support; and the voter can do nothing but stay silent about any other candidates. BPV relaxes this a bit, but merely by allowing the voter the added flexibility of picking (still for just one candidate) from either the acceptable candidates or the unacceptable candidates. Evaluative systems allow voters to register an opinion about any or even all of the candidates.
A simple example election that compares BPV with plurality voting should provide some important insights. A summary of this example is illustrated in the following table:
A small-town election with 20600 voters holds a plurality election, perhaps to choose the next mayor. Having always used plurality in previous elections, there is an established duopoly and in the election, the two duopoly candidates, D1 and D2, split the votes roughly down the middle. A third-party candidate makes an unusually strong showing with 612 votes, but D1 is declared the winner with 10130 votes, just 272 more than the total for D2. As usual, roughly half of the voters are disappointed with the outcome.
Now consider an alternative election held with BPV. Perhaps excited by the novelty of voting against a candidate, 145 of D1 supporters changed their vote to instead oppose D2. And 800 of the D2 supporters did likewise, in opposition to D1 rather than support for D2. In the vote tally, these changes in voting resulted in no change to the vote-count for the third-party candidate, TP, but neither was there any change in the numeric advantage of 272 votes enjoyed by D1 over D2; the vote tally for both duopoly candidates fell by 945.
This illustrates something inherent in the nature of BPV. Whenever a candidate changes from voting support for one duopoly candidate into voting opposition against the other, the margin of victory within the duopoly (in votes) is unchanged. When it is only the duopoly votes that change to opposition, vote tallies for the duopoly candidates drop by the total number of votes that changed; it makes no difference whether the vote change is from the D1 camp or the D2 camp. The margin of victory within the duopoly in percentage terms does decrease, but what is more important is that the margins of victory over the minor party candidates will diminish.
The only significant effect when a duopoly voter chooses to vote in opposition rather than support is an improvement in the prospects of third-party candidates. Aside from the novelty of it, why might voters opt for using the newly available opposition vote? In some cases, that decision might be because it seems more honest; the voter may really support neither duopoly candidate (and perhaps none of the other candidates either). But whatever the reason, the effect is simply to reduce the vote-count shared by the duopoly; the winner in that two-way contest is unaffected.
Switching just one duopoly vote to opposition only very slightly improves the chances for a third-party candidate. In this example, roughly half of the duopoly voters would need to switch to opposition voting in order for TP to win election. And this example is extreme in that the third-party candidate received nearly 3% of the vote, an exceptionally strong showing for a third-party candidate.
Whatever voting system is used, one election win is not enough; multiple wins outside of the two dominant parties would have to occur frequently to provoke a large number of voters into reconsidering their habit of simply ignoring third-party candidates. Perhaps opposition to the duopoly would be enough reason for this to happen, but it seems certain that the duopoly parties along with their big-money supporters would aggressively campaign to discourage casting opposition votes.
BPV does make it possible for a third-party candidate to win, but given an existing duopoly it seems doubtful that would happen on more than rare occasions. The odds BPV to put an end to duopoly do not seem favorable.
But BAV takes steps to actively penalize even a developing duopoly and that would greatly encourage third-party wins. If the two dominant parties are exactly equal in size, voters in one of those two parties will cancel the support votes from the other with the same number of opposition votes. With a vote tally of zero, a third party candidate should have good prospects for winning. Typically, there will be some imbalance in number of voters favoring those two parties so the expected outcome will be for one to retain a small positive net vote while the other has a negative net vote. Support or opposition votes by third-party voters would likely force additional variations from this prediction, but presumably there would be only a few of these votes. It seems unlikely that most of these voters would probably vote in opposition to both duopoly candidates, further reducing the vote tally for both duopoly candidates.
Penalizing polarization in the manner of BAV is a feature that is common to balanced evaluative voting systems. While several balanced voting systems have been discussed in the earlier articles in this series, the only evaluative examples come from among the balanced-score voting systems; BAV is the simplest of these. It is unfortunate that with the exception of BAV, these other score systems seem unacceptable because they invite a strategic attack. Even so, adoption of any of these balanced evaluative voting systems would assist nascent third parties win elections. That should raise the expectation for third-party and independent candidate election victories to rise and it seems duopoly would fade away. In time the notion of "the other party" would seem likely to be regarded as quaint or even nonsensical.
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