Diving Into Our Straw Poll Data: Min/Max Voting

Our June 30 10th CD Straw Poll gave voters the opportunity to use three unique voting methods—score, approval, and plurality voting—simultaneously on the same four-candidate congressional race. This gave us the opportunity to directly compare how voters interacted with each ballot.

In part one of this series, we looked at bullet and anti-voting. In part two, we’re exploring min/max voting.


Min/max voting, like bullet voting, is when a voting method gives voters the option to cast a nuanced vote and they choose not to. Specifically, it's when voters strategically choose to only use the top and bottom scores on a score voting ballot, making it functionally equivalent to approval voting.

Min/max voting is often raised as a concern with score voting but, as with bullet voting, our data do not show voters behaving that way.

None of our straw poll participants gave multiple candidates maximum scores, let alone maximum scores for multiple candidates with minimum scores for all others.

The closest ballot in our straw poll to an actual min/max ballot

The closest ballot in our straw poll to an actual min/max ballot

A hypothetical example of a min/max ballot. There were no actual min/max ballots in this straw poll.

A hypothetical example of a min/max ballot. There were no actual min/max ballots in this straw poll.

Indeed, we did not find any min/max ballots unless we expanded the definition of “min/max” to mean “ballots using only two unique scores.” Under that expanded definition, we found one ballot marked 4/4/1/1, which used neither minimum nor maximum scores—a min/max voting rate of 2.6% (1/38). Adding that generously defined min/max ballot to the generously defined bullet votes described in part one of this series brings the total rate of bullet and min/max voting up to 18.4% (7/38) on our straw poll score voting ballots.

Compared to IRV

While our straw poll bullet and min/max voting rates might differ with a full election’s worth of ballots (95% confidence interval of +/- ~10%), they are comparable to demonstrated rates of bullet voting under instant runoff voting. Our data show such behavior in the mid- to high-teens, while the 2018 Democratic congressional primary in Maine showed a 23.6% bullet voting rate under their new instant runoff voting system.

A comparison of strategic voting using instant runoff and score voting

A standard chi-squared test of similarity used to compare our data against the Maine congressional primary data failed to demonstrate a significant difference between the two rates of bullet voting (p-value 0.122087), nor min/max voting (p-value 0.231101). In other words, while our data showed fewer cases of bullet and min/max voting than were seen in Maine, you would get similar results somewhere around 12–23% of the time simply by pulling random ballots out of the Maine data. That implies that bullet voting and/or min/max voting is less a question of voting method and more likely simply how voters choose to behave.

Expressiveness and Score Voting

On the other side of the argument, while only three straw poll participants used exclusively the maximum and minimum scores, there were four participants who indicated they felt that no candidate deserved a maximum score nor a minimum score. An additional 12 voters chose to use the maximum or the minimum score, but not both. Four of those 12 voters still ended up using a distinct score for each candidate.

Of the 21 voters who used the full available range of scores, 12 used a distinct score for each candidate.

For further evidence that voters prefer to be expressive with their ballots, we took a look at the scores themselves. Out of the 150 scores marked across 38 ballots, less than half (46.0% or 69/150) were “maximum” or “minimum” scores (5 or 0, respectively). While it is expected that voters would tend to include candidate scores at maximum or minimum, the fact that a majority of scores were neither implies that, within the established bounds, voters honestly evaluated the candidates.

Looking at the individual ballots, see similar results, with 16 ballots total giving each of the four candidates a distinct score (42.1%) and an additional 15 ballots providing three distinct scores (39.5%).

Score distribution by candidate in CD10 Straw Poll

Voter expressiveness on CD10 Straw Poll Score Ballot

Those are promising findings, as simulations show score voting performs even better when the majority of voters are honest, outshining nearly all other voting methods for single-seat races.

Read more about our straw poll here and check back soon for more analysis of our straw poll results, including subjective scales and favorite betrayal.