This article re-visits a balanced voting system and compares it to BAV. In the process, the roles of being balanced and evaluative are revealed more clearly. The article can also be taken as a review of the most important features of BAV.

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Plurality voting is frequently maligned, but it truly is a superb voting system provided there is a maximum of two candidates. That is a serious restriction, however, that makes this voting system a poor choice for our elections. Unwise as it is, we continue to rely mostly on plurality voting.

When there is an established duopoly, the reality is that additional candidates beyond the two from the duopoly have no realistic chance of winning. But these other candidates can upset an election by drawing away votes from candidates who otherwise would have won and for that reason, these extra candidates are frequently called spoilers. But derision this implies is misplaced; having these extra candidates is a good thing; plurality voting deserves the blame for these spoiled elections, not the extra candidates. Plurality voting simply is not up to doing the job it is assigned.

We feel faced with a dilemma. Frequently, movements are convinced that, against all odds, they can be the exception to win election against the duopoly; and consequently, elections are spoiled. While we would prefer to have more candidates and to give voters more choices, but having a duopoly ensures that extra candidates beyond the two duopoly ones will surely lose and possibly trigger a spoiled election.

It might seem excessively optimistic to hope for finding a better voting system. But perhaps there is one that not only accommodates, but even encourages elections to have more than just two viable candidates? The word viable is important here; a viable candidate is one with a realistic chance of winning election. Adopting such a voting system would seem to be a way to have more candidates and to end the duopoly. Happily, as simple a voting system as it is, balanced approval voting (BAV) does exactly this. As a bonus, adopting BAV makes voting easier.

Voters find it challenging to compare the virtues and vices of candidates with one-another to make a judgement as to which candidate they prefer; consequently, many voters bypass such efforts and simply rely on the simple test of party affiliation. Also, there could be several candidates who seem so similarly qualified that choosing just one can seem impossible. With BAV there is no need for an individual voter to make such problematic comparisons and choices.

With BAV, voters are asked simply to designate candidates as either acceptable or not acceptable. Voters who want to neither support nor oppose, perhaps, an unfamiliar candidate are encouraged simply to skip over that candidate as a way to avoid registering an opinion. In essence, voters are asked to divide up the candidates into three categories: the good, the bad and the others.

Voting with BAV does not just seem easy, it is easy; with little effort, voters become aware of which candidates they would be content to see win and which they would prefer to see lose, and all they need to do is just put that information on the ballot. Of course, having hundreds of candidates would make such voting a tedious chore, but a preliminary election could trim the number of candidates to a more manageable size, perhaps somewhere between six and twelve.

Sometimes an objection is raised that BAV violates the principle of One Man, One Vote (OMOV). The same objection would surely apply just as appropriately to approval voting, to ranked choice voting or in fact most other alternative voting systems that have been proposed. But OMOV is surely not one of the ten commandments, the Supreme Court has not yet exposed it to be in the Constitution and it is not a law of nature. There is no identifiable authority insisting on it nor is there a study suggesting it to be an important issue. OMOV seems merely to have been penned as a catchy phrase for demonstrators to chant, probably during a campaign for expanding the right to vote. Still, that would be a long time ago and we now live in a world that has changed considerably.

That concern aside, OMOV lacks clarity because the word, "vote," is ambiguous when used as a noun. It could refer to any single mark on a ballot (in which case OMOV would forbit addressing multiple issues in an election). At the other extreme "vote" could be interpreted as the aggregate of all of the marks on a ballot. Generally, the meaning falls somewhere between these two extremes, with the exact shade of meaning left to be inferred from context. It seems ironic to think that possibly an ambiguous chant, penned long ago for a campaign to improve democracy, to now be invoked instead to keep voters from adequately expressing their opinions.

In the second article of this series, we introduced a voting system, B1, which arguably seems simpler than BAV. That was useful name to use in that article a decade ago, but this is a different time and a different article and at this time I favor a more descriptive name, balanced plurality voting (BPV). An organization that promotes adopting BPV often refers to it instead as the negative vote.

BPV insists (just as does plurality voting) that the voter express an opinion regarding only a single candidate on the ballot. Of course the voter is free to choose which candidate to evaluate but, once chosen, the BPV voter can specify either support or opposition for only that candidate.

Unfortunately though, when there are more than two candidates, making this choice of candidate can be a challenge. After all, a voter is apt to agree with any specific candidate on some issues but not on others and both the issues and positions vary from one candidate to another; there can be a whole host of different issues to consider. While BPV probably makes election administration fairly easy, but when there are several candidates BPV can make voting a serious challenge.

A voter who does find the choice difficult may feel forced to just choose one candidate arbitrarily. But this is vote-splitting, precisely what triggers the spoiler effect. And this variant of vote-splitting could likewise trigger erroneous election outcomes.

Alternatively, such voters may base the decision on some inappropriate consideration (electability for example). Making decisions in this way is a most harmful form of strategic voting. It clearly tends to corrupt an election by preventing ballots from reflecting opinions about the candidate. Perhaps the greatest deficiency of plurality voting when there are multiple candidates is the limitation on voters to express an opinion about just one of them. BPV adopts this same deficiency.

Unfortunately, an all too common feature of voting systems is favoritism on the basis of name recognition (fame). Balanced voting elections seem unique favoring neither the famous nor the less famous; both BAV and BPV are balanced systems, and it follows that both systems avoid this so common hazard. It would be possible to structure other voting systems so that the imbalance would favor the least famous candidates, but somehow the structural thumb on the electoral scale always seems to be in the other direction, consistently to favor the most famous candidates. Favoring the famous in elections is a problem because it helps to perpetuate a duopoly (whose candidates are famous, if only by the very fact of that nomination).

While BPV is balanced, it fails to be evaluative. An evaluative system (such as BAV) asks a voter to answer the very same question for each candidate. This allows voters to judge each candidate on individual merit rather than in any comparison with others; voters are not asked to choose one (or more) candidates for special treatment nor are they asked to rank the candidates relative to one another. Using an evaluative voting system, a voter can (and should) vote exactly the same for two candidates whenever that voter feels the two are (roughly) just as acceptable. This way, voters can express in considerable detail their willingness to compromise with other voters. The evaluative nature of BAV gives voters a way to influence the compromise with other voters in choosing a winner. Encouraging such compromise is uniquely a feature of evaluative voting systems like BAV and approval voting.

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.

Authors Bio:

Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. Taught for several years at Lehigh University prior to a short stint at Bell Laboratories but followed by a much longer career at NEC punctuated by ten U.S. and international patents in the general area to semiconductor applications.

Now living in a comfortable Maine retirement community and focused on the prospect of upgrading democracy by means of an improved voting system.