Elections — How do the numbers stack up?
Fairness and democracy is core to our society. How can we use math to make our elections more fair?
Since Ancient Greece, democracies have played a pivotal role in shaping our governments. However, recent elections in the USA have begun to question the current system of voting, in particular the electoral college.
The Electoral College
“Experts who study the math agree on one thing: The electoral college system used to decide US presidential elections is one of the worst.” — Wired Magazine
The electoral college is a system in which the citizens’ votes are represented by groups of ‘electors’ who make up a ‘college.’ Electors cast a vote for the president based on the ballots of their constituents. Each of the 538 electors can cast a single vote and a total of 270 votes for a candidate is required to declare them a winner.
Each state has a number of electors representing their population, and the electors generally, but not necessarily, vote the winner of the poll in their county. So if a candidate wins a marginal victory or a landslide victory, they get the same number of electoral votes. This means that it is possible the president does not get the majority national vote, as occurred in 1824, 1876, 1888, 2000 and most recently in 2016. Maine and Nebraska are the only 2 states that vote in the electoral college according to the proportion of votes for each candidate.
This system of voting creates the formation of so-called ‘swing states’. These states tend to be undecided before the election, and thus presidential candidates tend to focus their efforts on these states rather than on the nation as a whole. For example, in 2016, Donald Trump won the presidential election, despite having 3 million fewer votes than Hilary Clinton, due to victory in several ‘swing states’, like Pennsylvania.
However, this method is only used in the USA, and there are several other methods touted as better, fairer and more accurately representative.
Plurality
Each person has a single vote, and the candidate with the majority is declared the winner. This is used in most democracies worldwide.
Pros: One person One Vote. In a two candidate election, the voters will always vote for their favorite candidate.
Cons: Voters may abandon their favourite candidate in fear of ‘wasting’ their vote. This can influence the outcome of the election to let second favorites win rather than actual favorites.
Cumulative Voting
Each person has a set of votes (eg. 10) to distribute however they choose amongst the candidates. For example, 6 to one candidate, 2 to one and 2 to another. Used in some jurisdictions in Alabama and Texas and many corporate boards.
Pros: You can vote proportional to your support
Cons: Voters often strategize their distribution. Distributing your votes according to your support may hurt the chances of your favorites, and lead to the candidate you don’t want winning. But putting all votes for a single candidate faces the same problems of a plurality system.
Instant Runoff
Each person ranks their candidates. The top choices are tallied and if a candidate has a majority they win, otherwise, the voter with the fewest votes is eliminated. The second choice of those that voted for the eliminated candidate are added to the tally and the process is repeated. This method is used in Australia, Ireland and San Francisco.
Pros: A accurate representation of voters than plurality to the reduction of extremes. Discourages negative campaigning as it could damage second choice votes.
Cons: Mathematic models show that voting for your favourite candidate may actually hurt their chances of winning, and ranking them lower can benefit their final results. This violates the monotonicity criterion, the principle that voting for your favourite candidate should always benefit them.
Approval Voting
Each person votes for every candidate they consider acceptable. This method is used in many professional associations, eg. the Mathematical Association of America etc.
Pros: The final winner will be acceptable for the majority of people.
Cons: This system doesn’t separate a good candidate from a great one. Voters cast different numbers of votes and results can be unpredictable.
Borda Count
Each person ranks the candidates, with each rank given a number of points. Eg, first place 4 points, second 3 points etc. Used for polls in college basketball and football.
Pros: Theoretically eliminates outcomes non-representative of voter intentions.
Cons: It is difficult for voters to differentiate between a single place in lower rankings eg. 5 and 6, and thus these rankings would be almost random. On a nationwide scale, millions of votes would then be arbitrary.
What do you guys think? Do we need to update our electoral system across the globe? Write in the comments which system you like the best.
Vedant Bahadur
