With BV-1, a voter in a polarized race with two major candidates may choose to vote for the candidate that the voter most prefers or possibly against the other major candidate. Choosing that second option improves the chances for some third-party candidate to win; each leading candidate's supporters and opponents may cancel each-other and this opens the possibility for a third-party win. With BV-1, whether to cast a positive or a negative vote is a choice that is forced on the voter.
The other balanced voting systems under discussion
allow a voter to cast two or more votes and in a polarized political
environment it is predictable how they will cast those first two
votes. Most voters will likely vote for the major party candidate
they prefer and they will use the second to vote against the other
major party candidate; in a polarized environment that seems like
getting to cast two votes for your favorite candidate, but with
roughly equal numbers of voters for both poles of the political
spectrum, the two major party candidates will net close to zero
votes. What seems to individuals to be voting twice for their favorite candidate turns out, when that choice is made by everyone, to open the door for a win by someone other than in the two major parties.
In an already polarized political environment, any of these multiple-vote balanced systems will disadvantage candidates of the major parties much more than BV-1 does. Given how accustomed we are to seriously polarized politics, we might well wonder whether this disadvantaging of the major party candidates to this significant a degree is a wise thing to do. Imposing BAV (or even BV-2) suddenly on an already polarized political environment would probably deliver quite a shock.
If instead, BV-1 were adopted for the first few elections, voters would have a chance to get accustomed to the notion that someone who is neither a Democrat or a Republican might be elected. Likewise the media would have a chance to come to the same realization and to begin informing the voters about other candidates. A the same time that polarization decreases, voters would become educated about about balanced voting. Initially, while there are a relatively few candidates, BV-1 should work well; eventually, as voters become accustomed to balanced voting and there are more candidates and the limitations of BV-1 become more apparent, BAV could be adopted in its place.
With BAV, just as with any other voting system, there is a distinct possibility of a tie or a near tie in any given election. Electing a candidate on the basis of one or even a few hundred votes is apt to result in hard feelings if not calls for recounts, protests and perhaps even law suits. If there are two or more candidates in a statistical dead-heat after a BAV election an option might be to have a runoff election but this time to take into account the first-choice preferences of the voters. A consideration in changing the voting method is that a runoff using the same method as before is apt to yield much the same inconclusive result. A second consideration is that the level of enthusiasm for a candidate really is important, though not as important as it is to respond to the wishes of the greatest number of voters.
But elections are expensive to conduct and they disrupt people's
lives so a decision to call voters to the polls a second time is not
generally a realistic option. Fortunately, there is another
possibility and that is to anticipate the possibility of such a
situation and prepare for it in the first (an only) ballot. This
need not require a complicated ballot. All that is needed is a third
column where the voter can check off which one candidate (For
or Against) is most important to the voter. 
In the event that there is a tie or a near tie in the first-round BAV count, there can be a runoff re-count using only those votes marked for use in the runoff. Of course there will be some votes marked for the runoff will not count because they are For or Against a candidate that was eliminated in the first-round BAV vote count, but these are from voters who have indicated a relatively low interest in the second round, given that their most favored candidate lost in the first round.
In both rounds of counting (should both be needed), the counting is balanced - opposition to a candidate weighs equally against support. With this two-stage approach, in the first (and possibly only) round of counting it does not matter how strongly a voter feels about a candidate; it is only the voter's judgment of approval or disapproval that counts at all. But in the second round of counting the factor of importance does enter importantly into the decision of which of the runoff-candidates is to win. But whichever candidate wins the runoff, democracy is well served because these runoff candidates have already been judged in the first round as (within a small margin of error) as being equally acceptable (on balance) to as large number of voters as possible.
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