A Justice Site
Local Hub Sites
Created: November 8, 2000
This multiple interpretations practice is based on the Presidential Elections 2000. It relates to the classification of data as nominal, ordinal, or interval and to what we sometimes call "throwing out data."
Here's how it works. We have a popular election for the President of the United States. We measure the decision each person makes about who should be President by votes. Each vote has the same weight and counts the same, no matter who casts the vote. Votes are fungible. That is, one vote is as good as any other vote.
We then count the number of votes each candidate receives. So votes are interval units that we can count. When we measure the popular vote by the number of ballots, that is interval measurement. Let's make a graph:
Figure 1 shows Gore and Bush neck and neck in the popular vote. Both are stretching their necks, reaching for 49 million. Votes are fungible. Every vote counts.
Figure 1. Popular Vote, Presidential Elections, 2000
Figure 2 represents jeanne's imaginary on what is causing this presidential election dilemma. I could have drawn the Gore and Bush electoral votes as rectangles, and we would have had a conventional bar graph. You might want to try that yourself. But I wanted to show the relationship and change that came with the switch from popular vote to electoral vote.
Figure 2. Electoral Vote, Presidential Elections, 2000
Popular vote was measured by votes, and interval measure. We could count the votes individually. But electoral votes are counted in groups or categories. Florida has 25 votes, and they go together. They cannot be split up into individual fungible votes. So winning the popular vote in one state is not fungible with winning the popular vote in another state. Wisconsin has only 11 electoral votes. This was done originally so that populous states would count more heavily that states with relatively few people in them. What has that done to our measurement?
Well, it's changed the way we are measuring from interval to ordinal. Florida counts more heavily with its 25 electoral votes than Wisconsin with its 11 electoral votes. When we switch to ordinal data what we are really doing is throwing out data. Where we could have looked at Florida more accurately by counting the actual votes, we, in fact throw away that extra information and count Florida as either win or lose, not as the number of actual votes won. Because we actually do record the number of votes, we can now go back and look at a graph representing that way of measurement, which we did in Figure 1 on the popular vote.
But if we know threw out the original votes and kept only the electoral results, we would never be able to reconstruct the first figure from the informatin contained in the second figure. We can always collapse categories as the electoral college does with states. But we can't re-expand those ordinal categories to the interval data of the actual vote count. This means that moving from interval to ordinal is the equivalent of throwing out information.
In the two figures you begin to see the loss of detail as we move to ordinal from interval.
Data Sources:Yahoo News provided the following data on the popular vote at Wed Nov 8 12:20 PM ET, and CNN provided the electoral vote count at the same time:
99% of the nation's precincts reporting:
- Gore 48,628,395 - 48%
- Bush 48,384,440 - 48%
- Others 3,698,994 - 4%
Needed to win: 270 of the 538 electoral votes (ev) from the 50 states and the District of Columbia.
Answer the following questions about the graphs:
- What effect does throwing out data have on the results?
jeanne's lecture notes
The results are less exact, and if the original data are not preserved, the information from the original, more exact, data cannot be retrieved. Let's say it would be a little like giving a grade to the class instead of to individuals. For some of you, that would be good news, because the class grade might be higher than your individual grade. But for those of you who did better individually the class grade might be lower than the grade you would have gotten otherwise. This is one reason people complain about working in groups. The result is often the lowest common denominator. And often in groups no individual grades are recorder, so we cannot retrieve any measurement of individual effort.
- So why come up with this technique of throwing out data?
jeanne's lecture notes
Because none of the ways in which we measure social data will stand alone. What does a vote mean? It might mean I don't like the person. It might mean that I like the values the person says he/she stands for. It might be a compromise with many things. And what does an electoral vote mean? It means that the popular vote of that state was won by at least one vote by the person who gets the electoral votes. But it also represents the legislature's way of trying to balance the powers of bigger and more populous states against the powers of smaller states. The same reasons we had for the House and Senate, remember?
- Is such manipulation of statistics "lying with statistics?"
jeanne's lecture notes
Not if we are upfront about the ways in which we are measuring and how those ways are valid within the objectives we have set. But if we're not upfront about the underlying assumptions, then, yes, I think that's at least "fibbing." And I fear that many people do not fully understand why and how we manipulate the figures. That means they may assume that "winning" means something very different from what we actually measured.