Poll Analysis: Clinton Versus Giuliani

This post is the first in a series of poll analyses for the 2008 elections. I am going to begin this series by looking at the result of state polls in which Hillary Clinton is matched up with Rudy Giuliani. Increasingly, Hillary Clinton looks to be the Democratic nominee for the 2008 presidential race. The Republican field is less certain, but Rudy Giuliani has been consistently out-polling his Republican challengers.

The analyses consist of Monte-Carlo simulations of elections based on the head-to-head poll data. I’ll begin this series by describing the methods in some detail, so that I can refer back to this post in subsequent analyses. (If you want to skip the methods, search below for “Results:”)

Methods:
Poll data

I have assembled a collection of state-wide polls in which Hillary Clinton is matched up, head-to-head with one or more Republican challengers. Typically, I find polls from the web sites of well-known polling firms. However, if there is sufficient information, a secondary source (e.g. news summary of a poll) might be acceptable.

The most common polling firms to release head-to-head polls so far are SurveyUSA, Rassmussen, and Quinnipiac. This initial batch of pre-primary head-to-head match-ups includes polls from Brown University, Texas Lyceum, Research 2000 and Mason-Dixon. No doubt, many, many more polls and polling companies will become available after the primary.

To be considered acceptable, each poll must come from a reputable pollster and must included the following information:

  1. The name of the polling firm
  2. The dates on which and state where the poll was taken.
  3. The number of individuals polled or, alternatively, the margin of error
  4. The number or percentage of individuals selecting Clinton
  5. The number or percentage of individuals selecting her opponent

The polling results are used to simulate elections, and then assign electoral college votes to a candidate. Here is how it works.

I begin with a range of dates for current polls. For example, I might accept all polls from 1 Sep 2007 to today (30 Oct 2007). [Update: I use the mid-date of when the poll was taken when determining whether a poll falls within the lower date bounds.] If a state has one or more polls in this date range, the total number of votes enumerated for a candidate is summed.

For example, there were two polls in this date range in Missouri, both conducted by SurveyUSA. The first poll, taken from 14 Sep to 16 Sep surveyed 545 individuals; 48% went for Giuliani and 45% went for Clinton. Hence, Giuliani gets 262 votes and Clinton gets 245 votes. The second poll taken from 12 Oct to 14 Oct surveyed 542 individuals; 43% went for Giuliani and 50% went for Clinton. Giuliani gets an additional 233 votes and Clinton gets an additional 271 votes.

The total of 495 votes for Giuliani and 516 votes for Clinton are used as the basis for simulated elections (described later).

Suppose there are no current polls in the date window. In that case, I use the most recent poll on record. There is no poll between 1 Sep and 30 Oct for Arkansas; but there was a Rasmussen poll of 500 individuals taken on 14 Aug. Therefore, the number of votes for Clinton and Giuliani in that poll would be taken as the best estimate in Arkansas.

Suppose there are no (known) polls whatsoever in a state. In that case, I assume the party that won the 2004 presidential election would prevail in 2008. Nebraska has no known polls with head-to-head match-ups, so I assume Giuliani always beats Clinton in Nebraska, since the 2004 presidential election gave Bush 65.9% of the vote and Kerry 32.7% of the vote.

One other comment about polls. Most reputable polls include the number of individuals sampled. So far, all polls have included this number. But, some polling firms do not publically release the number. When a 95% margin of error (MOE) is provided, I estimate the number of sampled individuals as (0.98/MOE)2. (This is based on the standard error of a binomial distribution and, as commonly done by pollsters, assuming the true proportion for each candidate is 0.5.)

Simulations

After all the numbers are collected for each state (plus Washington, D.C.) with at least one poll, many (typically, 10,000) elections are simulated.

For each election, I simulate voting in each state (plus D.C.). In the Missouri example described above, there were 1,011 (= 495 + 516) individuals sampled. Empirically, 51% went for Clinton and 49% for Giuliani. Therefore, I simulate 1,100 votes being cast, each time drawing a random number between 0.0 and 1.0. If the random number is between 0.0 and 0.51, the vote goes to Clinton. If the random number is between 0.51 and 1.0 the vote goes to Giuliani.

If the state election results in a tie, a coin is tossed for the winner. The winner of the vote gets the electoral college votes for that state. (Maine and Nebraska use a different method of assigning electoral college votes, so if polling data become available for these states, I’ll have to cobble together some way of incorporating potential splits. Without polling data, I am using the 2004 result in which all 4 Maine votes went to the Democrat and all 5 Nebraska votes went to the Republican.)

One simulated election is completed after all 50 states and D.C. have been processed. After all elections have been processed, the electoral college votes are plotted and some basic statistics are computed.

Results:

I’ll show the results of three series of simulated elections between Clinton and Giuliani. The first series includes all poll results I’ve found for 2007. The discussion picks up after the table:

After 10000 simulated elections, Clinton won 7065, Giuliani won 2702, and there were 233 ties.

Average [SE] EC votes for Clinton: 285.1 [ 23.6]

Average [SE] EC votes for Giuliani: 252.9 [ 23.6]

Median [95% CI] EC votes for Clinton: 283 [246, 331]

Median [95% CI] EC votes for Giuliani: 255 [207, 292]

State # polls Total Votes %Clinton %Giuliani Clinton %wins Giuliani %wins
Alabama 3 1482 44.9 55.1 0.0 100.0
Arkansas 1 460 59.8 40.2 100.0 0.0
California 3 1392 58.5 41.5 100.0 0.0
Colorado 1 450 44.4 55.6 1.5 98.5
Connecticut 3 3458 49.5 50.5 29.2 70.8
Florida 12 10290 48.8 51.2 0.0 100.0
Illinois 2 875 53.7 46.3 98.7 1.3
Iowa 3 1462 51.7 48.3 91.4 8.6
Kansas 3 1436 43.9 56.1 0.0 100.0
Kentucky 3 1491 48.2 51.8 7.9 92.1
Massachusetts 2 998 59.9 40.1 100.0 0.0
Michigan 2 870 55.2 44.8 99.9 0.1
Minnesota 3 1511 54.5 45.5 100.0 0.0
Missouri 4 1961 50.5 49.5 71.4 28.6
Nevada 2 1110 45.3 54.7 0.0 100.0
New Hampshire 2 924 51.1 48.9 76.0 24.0
New Jersey 7 7648 48.6 51.4 0.0 100.0
New Mexico 3 1425 50.9 49.1 79.4 20.6
New York 9 7826 57.8 42.2 100.0 0.0
North Carolina 1 435 49.4 50.6 38.7 61.3
Ohio 15 12378 50.8 49.2 100.0 0.0
Oklahoma 1 463 48.4 51.6 22.4 77.6
Oregon 3 1394 51.1 48.9 82.4 17.6
Pennsylvania 10 9116 48.9 51.1 0.0 100.0
Rhode Island 2 877 61.7 38.3 100.0 0.0
Tennessee 1 450 51.1 48.9 70.6 29.5
Texas 1 632 49.2 50.8 31.8 68.2
Virginia 5 2305 50.2 49.8 59.1 40.9
Washington 2 937 51.9 48.1 87.7 12.3
Wisconsin 4 1899 51.6 48.4 92.4 7.6

When all 2007 head-to-head polls are considered, Hillary Clinton beats Rudy Giuliani most of the time. Should the candidates tie, the House would most likely adjudicate the election for Clinton. (Currently, the Democrats control 26 state delegations, and the Republicans control 20 state delegations.) Therefore, if the polls reflected a static preference for the 2008 candidate, Clinton would have a 74% chance of being elected President.

But preferences change with time. Look at what happens when we examine only polls taken from 1 Jul to today (discussion after the next table):

After 10000 simulated elections, Clinton won 10000, Giuliani won 0, and there were 0 ties.

Average [SE] EC votes for Clinton: 348.4 [ 22.8]

Average [SE] EC votes for Giuliani: 189.6 [ 22.8]

Median [95% CI] EC votes for Clinton: 347 [307, 394]

Median [95% CI] EC votes for Giuliani: 191 [144, 231]

State # polls Total Votes %Clinton %Giuliani Clinton %wins Giuliani %wins
Alabama 2 974 45.0 55.0 0.0 100.0
Arkansas 1 460 59.8 40.2 100.0 0.0
California 2 921 59.6 40.4 100.0 0.0
Colorado 1 450 44.4 55.6 1.4 98.6
Connecticut 1 1196 51.2 48.8 80.9 19.1
Florida 6 4634 50.3 49.7 65.9 34.1
Illinois 2 875 53.7 46.3 98.8 1.2
Iowa 2 953 53.5 46.5 98.9 1.1
Kansas 1 463 43.4 56.6 0.6 99.4
Kentucky 2 987 47.8 52.2 9.5 90.5
Massachusetts 1 489 63.4 36.6 100.0 0.0
Michigan 2 870 55.2 44.8 100.0 0.0
Minnesota 2 1001 55.9 44.1 100.0 0.0
Missouri 3 1456 51.2 48.8 85.1 14.9
Nevada 1 594 46.3 53.7 4.2 95.8
New Hampshire 2 924 51.1 48.9 76.1 23.9
New Jersey 3 2569 53.4 46.6 100.0 0.0
New Mexico 2 955 51.9 48.1 88.1 11.9
New York 5 3730 59.8 40.2 100.0 0.0
North Carolina 1 435 49.4 50.6 39.4 60.6
Ohio 8 5953 51.5 48.5 100.0 0.0
Oklahoma 1 463 48.4 51.6 23.4 76.6
Oregon 3 1394 51.1 48.9 82.8 17.3
Pennsylvania 4 3179 51.4 48.6 95.4 4.6
Rhode Island 1 468 65.8 34.2 100.0 0.0
Tennessee 1 450 51.1 48.9 68.9 31.1
Texas 1 632 49.2 50.8 33.5 66.5
Virginia 4 1829 51.0 49.0 83.8 16.2
Washington 2 937 51.9 48.1 87.0 13.0
Wisconsin 3 1423 52.3 47.7 95.9 4.1

So far, the second half of 2007 has witnessed a strong swing in favor of Hillary Clinton—so strongly that Giuliani doesn’t win a single simulated election out of 100,000! The biggest changes occurred in Florida, Pennsylvania, and New Jersey, which all shifted from solidly Giuliani to solidly Clinton. Connecticut also shifted from moderately Giuliani to moderately Clinton.

But pendulums swing and so do the attitudes of Americans. The final analysis includes polls conducted over the last month whenever possible.

After 10000 simulated elections, Clinton won 9989, Giuliani won 9, and there were 2 ties.

Average [SE] EC votes for Clinton: 341.2 [ 25.8]

Average [SE] EC votes for Giuliani: 196.8 [ 25.8]

Median [95% CI] EC votes for Clinton: 341 [293, 391]

Median [95% CI] EC votes for Giuliani: 197 [147, 245]

State # polls Total Votes %Clinton %Giuliani Clinton %wins Giuliani %wins
Alabama 1 491 45.8 54.2 3.4 96.6
Arkansas 1 460 59.8 40.2 100.0 0.0
California 1 453 58.5 41.5 99.9 0.0
Colorado 1 450 44.4 55.6 1.4 98.6
Connecticut 1 1196 51.2 48.8 80.9 19.1
Florida 3 2169 50.6 49.4 77.5 22.5
Illinois 1 435 51.7 48.3 77.7 22.3
Iowa 1 467 52.7 47.3 89.0 11.0
Kansas 1 463 43.4 56.6 0.6 99.4
Kentucky 1 489 51.1 48.9 70.8 29.2
Massachusetts 1 489 63.4 36.6 100.0 0.0
Michigan 1 425 55.3 44.7 98.2 1.8
Minnesota 1 491 56.0 44.0 99.3 0.7
Missouri 1 504 53.8 46.2 95.8 4.2
Nevada 1 594 46.3 53.7 4.0 96.0
New Hampshire 1 504 50.0 50.0 50.1 49.9
New Jersey 2 1339 52.1 47.9 93.9 6.1
New Mexico 1 471 49.5 50.5 39.8 60.2
New York 2 1391 61.5 38.5 100.0 0.0
North Carolina 1 435 49.4 50.6 39.3 60.7
Ohio 3 1732 51.7 48.3 92.8 7.2
Oklahoma 1 463 48.4 51.6 22.3 77.7
Oregon 1 496 52.6 47.4 89.1 10.9
Pennsylvania 1 790 53.3 46.7 96.4 3.6
Rhode Island 1 468 65.8 34.2 100.0 0.0
Tennessee 1 450 51.1 48.9 69.3 30.7
Texas 1 632 49.2 50.8 33.0 67.0
Virginia 2 926 49.5 50.5 34.8 65.2
Washington 1 463 53.8 46.2 95.1 4.9
Wisconsin 2 942 52.3 47.7 92.3 7.7

By eliminating polls taken from July, August and September whenever an October poll exists, we see a small shift in favor of Giuliani, in which he goes from zero to nine wins out of 10,000 simulated elections. Clinton’s electoral college vote tally shrinks slightly from a median of 347 to 341. Clinton loses a bit of ground in Illinois, Ohio, and New Hampshire, but gains ground in Missouri and Washington. She loses New Mexico altogether, although Kentucky flips from solid Giuliani to moderately Clinton.

Clearly many things can change between now and November, 2008, but Clinton is starting in an exceptionally strong position.

One other observation. Imagewise, the two purtative candidates started at very different places. The Republicans have suspected for seven or eight years that Hillary Clinton would eventually run for President. And they have used that time to frame her negatively to their base. Giuliani’s folk-hero image, on the other hand, was almost entirely constructed around 9-11. The Democrats have only started deconstructing the Giuliani image.

Therefore, I think the Clinton image has a lot more room for upward growth than does the Giuliani image.

Giuliani does have some room for growth, however. Right now, resentment (or downright hatred) of Republicans must be near all time high because of George Bush and his administration. After the primary, Giuliani (or whoever wins the GOP nomination) will have to create distance from the Bush administration in a big way. On the other hand, given the extremely hawkish rhetoric Giuliani is roped into using in order to win the GOP primary, distancing himself from Bush in a meaningful way after the primary is going to be rather difficult.

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