How Not To Waste Your Vote: A Mathematical Analysis

During this especially contested election, a lot of people are talking about people “wasting” or “throwing away” votes. However, many people who say this do not have a complete grasp of the full mathematical picture – or worse, they are only mentioning the part that supports their position. First let’s define what a “wasted” vote is.

Mathematical Definition of Wasted Votes

A wasted vote is a vote that provides no determination or effect on the final outcome of the election. According to Wikipedia: “Wasted votes are votes cast for losing candidates or votes cast for winning candidates in excess of the number required for victory. For example, in the UK general election of 2005, 52% of votes were cast for losing candidates and 18% were excess votes – a total of 70% wasted votes.”

There are two kinds of wasted votes that mathematically have no effect on the final election:

  1. Votes cast for candidates who did not win
  2. Excess votes cast for winning candidates

Clearly, neither of these kinds of votes statistically affect the election. However, many arguments only mention the first type without mentioning the second. Mathematically and logically, both categories are ineffectual votes.

First Past the Post

The value of your vote is what you give it. Should you spend it on a candidate you don’t believe in?The United States, along with several other nations, uses the First Past the Post (FPTP) or “winner take all” election. This method is defined as “the candidate who receives more votes than any other candidate wins.”

This is one of the reasons that many people mention wasted votes – our system creates that result. Sociologically speaking, the FPTP system tends to favor a two-party system. The French sociologist Maurice Duverger created “Duverger’s Law” which says just that.

The Electoral College

For U.S. Presidential elections, a state-by-state system is used called the Electoral College. Each state gets a proportional amount of electoral votes which are then used to find a majority for president. Interestingly, what happens in each separate state is a smaller FPTP election, followed by a counting of electoral votes.

The Electoral College is slightly different from a pure FPTP system because it requires an actual number threshold (currently 270 electoral votes) for a candidate to win instead of a simple majority of the votes.

We can sum things up as follows:

  1. States hold “winner take all” FPTP elections for electoral votes
  2. Electoral votes are counted
  3. The winner must have 270 electoral votes
  4. If there is no candidate that reaches it, the House of Representatives chooses the president

These distinctions are important, because they can change the math and the concept of the “wasted” vote phenomenon.

Wasted Votes in Presidential Elections

The general concept that is proposed by many is that you must always vote for a Republican or a Democrat because you must stop the worst candidate from winning. In a sense, you are voting a negative vote – against someone – rather than for a candidate of your choice. However, this actually depends on the scenario of the vote. Let’s look at some examples.

Bush vs. Gore: 2000

People voting out of fear of the worst candidate is a self-perpetuating cycle. Let’s examine a common example used in this discussion.

Following the extremely close 2000 U.S. presidential election, some supporters of Democratic candidate Al Gore believe that one reason he lost the election to Republican George W. Bush is because a portion of the electorate (2.7%) voted for Ralph Nader of the Green Party, and exit polls indicated that more of these voters would have preferred Gore (45%) to Bush (27%), with the rest not voting in Nader’s absence.

The argument for this case is even more pronounced because the election was ultimately decided on the basis of the election results in Florida where Bush prevailed over Gore by a margin of only 537 votes (0.009%), which was far exceeded by the number of votes, 97,488 (0.293%), that Nader received. (Wikipedia)

At first, this may look like a clear example of the need to vote for a major party. However, let’s break this situation down mathematically. In every single state election, Bush or Gore won. There were millions of mathematically wasted votes in this election of both types.

In California, Gore won by 1,293,774 votes. Mathematically speaking, there were over one million wasted votes for Gore in this state alone. None of these excess votes could have helped Gore, since he had already mathematically won the state. The California votes didn’t matter in Florida. In fact, the votes in Florida have much more relevance than any other state.

Conclusions: Sometimes a vote for a major party winner is wasted anyway. Sometimes everything will come down to one state. However, there is no way to predict in advance which votes will be this important. If the parties knew that Florida would have been the deal breaker, then they would have acted differently. However, we simply don’t know the future well enough to predict that.

We do know that battleground states are generally more important than “safe” states for each candidate, but it is hard to know exactly which state might matter. (There are plenty of scenarios you can research online about possibly electoral outcomes, I encourage you to do so.) This leads us into our next example.

Clinton vs. Trump 2016

Let’s do some math about the state of California and our current presidential election. The average RCP poll has Hillary Clinton ahead by 22.2 percent. The registered voters in California add up to 17.7 million. Not all of them will vote, but we can use the 2012 presidential election as a predictor, where 13.2 million people voted.

Out of those 13.2 million, according to current predictions, 52.6% will vote for Clinton. However, Clinton only needs about 31% to beat Trump. The other 21% of excess votes for Clinton will be wasted. This means that approximately 3 million votes for Clinton in California will be wasted. Now, this is only a mathematical model, but we have several reasons to believe in it.

  1. California has a history of being a heavily Democratic state
  2. Polls usually swing within a single digit margin of error
  3. 21% is quite a large margin of leeway

Even if the polling changes significantly, we are still looking at millions of wasted Clinton votes in California.

Now let’s throw Jill Stein into the math. As part of the Green Party, she is to the left politically of Hillary, so we will assume that votes for her will be taken from Clinton’s pool. (Though this isn’t always a true assumption, as we will see later.) Right now she is polling at around 4%, but we could even give her 5%. If you take away 5% from Hillary’s margin of 22.2%, that leaves a huge margin of 17.2%: still millions of votes. The takeaway from this: you can safely vote for Jill Stein in California without fear of changing the state election results. Therefore, it will not affect the national vote either.

Since we have the Electoral College, your votes will have no influence beyond the state to change other vote counts. Those who prefer Jill Stein can with a clear conscience vote for her, since it will make no difference mathematically. Later

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