“Results brighten hopes for GOP” read the headline, but
did they really? From a mathematical viewpoint, they simply confirmed
what voting theory tells us: Once you have more than two candidates in an
election, the voting method matters.
Gavin Newsome ran away with the race for Lieutenant
Governor, winning 49.5% of the vote and leading Ron Nehring who was the choice
of 23.5% of the voters. In the Secretary of State race Democrat Alex
Padilla held only a 0.1% lead over his closest challenger Republican Pete
Peterson (30.0%-29.9%). Even better for the GOP in the Controller’s race
where, as of this writing, the top two vote getters were Republicans Ashley
Swearengin (24.7%) and David Evans (21.6%), with Evans a scant 660 votes ahead
of the leading Democrat John Perez.
Things get more interesting, however, if we reduce the
question to how many votes each political party won, regardless of how those
votes were split amongst the candidates. Then, the Democrats win all
three races: 48.1% to 46.3% in the Controller's race, 51.6%-36.4% in the
Secretary of State race, and 55%-40.3% in the Lieutenant Governor race.
In November, there will only be two candidates. For the moment, assume that Green Party
voters would prefer a Democratic candidate to a Republican one, while everyone
that didn’t vote Green or Democratic would prefer a Republican candidate. If the ballot for the Controller position
were to have included a Democratic candidate, then these assumptions mean the
Democrat would win the general election 53.7% - 46.3%. Under the same
assumptions, the election for Secretary of State (54.5% - 45.5%) and Lieutenant
Governor (57.3% - 42.7%) will be cakewalks for the Democrats. But wait, this means that in all three cases
the Democratic candidate would win by more than 7%, albeit Gavin Newsom might
be the only true landslide.
So what does mathematics have to do with this? Voting theory, or social choice theory, is
the study of voting systems and their
effects and lies in the scholarly areas of mathematics, economics, and
political science. The first academic
writing on voting theory appeared in 1300, but its modern history started in
1700 with Jean-Charles de Borda and the Marquis de Condorcet debating over the
best method to elect members to the French Academy of Sciences. Later Charles Dodgson (Lewis Carroll) was one
of many 19th century English mathematicians that looked at voting
theory and wondered how best to choose a sole victor. In the
20th century, Kenneth Arrow proved his impossibility theorem that
states that any voting system with more than two candidates must violate at
least one intuitively desirable criteria.
This led to the Gibbard-Satterthwaite theorem that every system is
subject to strategic voting.
The California blanket primary (a run-off system) can run
afoul of vote-splitting, and this primary made that apparent. The most important candidate in the
Controller’s election was spoiler Tammy Blair, who split the Democratic vote, not
David Evans. Assuming that Blair’s voters would have preferred any Democrat by
a little more than a 2-1 margin had she not been on the ballot, then either
John Perez or Betty Yee would definitely be in the final election. However, as mentioned above, we may have no
Democrats on the November ballot for the Controller despite of the fact that
voters preferred some Democrat by 2%.
Since the party preference of the candidate according the original
proposition 14 is simply the candidate’s voter registration, a party might try
a form of strategic nomination. That is, they would encourage spoiler candidates
from the other party to run.
Strategic voting
may have occurred in the Controller’s race too.
Republicans favoring Swearengin may have risked voting for Evans
precisely to create a situation where Swearengin doesn’t have to face a
(potentially) stronger Democrat. To do
so would have been a pretty gutsy move though since Swearengin’s path to the
November ballot was not safe.
While we can’t be sure that the number of candidates on the
ballots had a significant effect on the final outcome in November, it may have had
a dramatic effect in at least the Controller’s race. After all, in the statewide races with party
affiliations, the percent of the ballots going to Democratic candidates ran
from a low of 48.2% to a high of 55.1%, while the percent of ballots going to
the Republicans ran from 36.4% to a high of 46.2%. While that last number might be of some
solace to Republicans, it still leaves them a long way from a majority.
