Election results can be presented very differently by simply changing phrasing. When journalists, pundits and the general media use the terms “points”, “percentages”, “percent more”, and “percent of” interchangeably, the lack of consistency results in distorted perceptions from the same numbers. People tend to underestimate the difference in vote share when using point spreads because of its linear nature representing an exponential behavior. This effect becomes more exaggerated when looking at smaller portions of the vote share that typically go to third party candidates.
The share of the votes each candidate receives is the percentage of the total votes cast in the entire election. We can look at the 2012 U.S Presidential election for a demonstration of this.
Approximately 129 million votes were cast for the presidential race of which Democratic incumbent President, Barack Obama, received 66 million and the Republican challenger Mitt Romney received 61 million. That adds up to 127 million votes. The remaining 2 million were cast for third parties. These results show that Obama won by approximately 3.9 points, but won 8% more votes than Mitt Romney. In other words, 8% more people voted for Barack Obama than Mitt Romney, but Barack Obama won 3.9 more points of the total vote. How does this work?
The victory represented by points does not directly compare the numbers of the votes counted. Instead, points mean the difference of the vote share each candidate received from the total. Obama won approximately 51% of the total vote share while Mitt Romney won 47.1%. The difference between these numbers shows the 3.9 point spread while the number 66 million is 8% more than 61 million. The point methodology is often phrased as percent. Be careful to clarify if using the term “percent” to describe this result. To observe this effect at a more extreme scale, it makes sense to look at third parties. Suppose the 2 million remaining votes that went to third party candidates had a distribution such that one candidate received 1.5 million and the other received 0.5 million votes. The difference in their vote share would be just 0.8 points, but the candidate receiving 1.5 million votes would have 200% more votes (three times as much). This demonstrates how using points and percentages inconsistently can create different perspectives of elections.
When using points, the difference is compared from the total vote and thus has a smaller number than when compared from the vote of one candidate. In a hypothetical election of just two candidates, a vote share spread of 10 points (45% vs 55% ) means the winner received 22% more votes. A 33 point spread (~33.3% vs 66.6%) means the winning candidate is receiving 100% more votes (twice as much). We begin to see how a 10 point win is actually a decisive win.
The graph above displays the relationship between points and the percentage gain of the winning candidate starting from a 2 point spread to a 60 point spread. The orange line is not necessary, but is included to show a linearly expanding point spread. Its values are identical on the horizontal and vertical axis for easier visualization. The blue line is the percentage gain of the winning candidate relative to the point spread depicted on the orange line.
On the far left, the spread is only 2 points which means the candidates received 49% and 51% of the total vote. This is shown on either axis and the orange line as stated earlier. The blue line shows that roughly 4% more votes were cast for the winning candidate at the 2 point spread. The graphs ends at a 60 point spread which means the candidates won 80% and 20% of the vote total. The 60 point difference means the winning candidate won 300% more votes (4 times as much). Once the spread approaches close to 100 points, the percentage approaches infinity. For visualization purposes, the graph doesn’t go further since the orange line would merge with the horizontal axis and become invisible.
As stated earlier, at a mere 10 point spread, the winning candidate would receive ~22% more votes than the losing candidate. This is why point spreads can be deceiving when confused with percentages. It often makes an election appear closer than it really is. This is not the only way of looking at the results.
In a hypothetical 10 point spread mentioned above where one candidate receives 45% (candidate A) of the vote share while the other receives 55% (candidate B), we can phrase the numbers four different ways:
Candidate A received ~82% of the vote of Candidate B, an ~18% decrease from Candidate B.
Candidate B received ~122% of the vote of candidate A, a ~22% increase from Candidate A.
There is a difference between saying candidate B received 122% more votes and 122% of the votes. In the former case that would be 2.22x as many votes while in the latter case that would be 1.22x as many votes.
In the most recent presidential election, former Secretary of State Hillary Clinton received 2% more of the national vote than Donald Trump. This 2% number comes from the point spread, not the percentage more votes that the former Secretary received (which is about 4.5%).
In 1984 when Ronald Reagan won 58.77% of the vote compared to Walter Mondale’s 40.56%, the spread was 18.21 points. Reagan, however won 45% more votes than Walter Mondale.
Remember that one method presents results by comparing the votes of a candidate to the total votes cast. The other method compares two candidates directly, regardless of the total. The former method is usually referred to as “points” while the latter is “percent.” Whichever method is used, consistency and clarification is the key. By slightly changing phrasing or using a different number as a comparison base, the public’s perception of an election result changes.
