More Probability and a Public Poll

In yesterday's article, I covered the probabilities associated with invalid votes and how their inclusion (or exclusion) could alter the outcome of the election. Today, I take it one step further by breaking down the math by district; either precinct, county or municipality depending upon the data set.

I'll explain the math first, and then I'll present the results. Today's formula arises from the same paper I previously covered, but this formula is slightly more complex.

Analysis by subdistricts.

If ki votes are removed in the ith district, an elaboration of the global analysis shows that the condition for a reversal is that an approximately standard normal variable z will exceed the constant.

Source: Mathematical Probability in Election Challenges via [PDF]

Using this information and what we already know from the previous article, we can determine the probability of a given number of errors, across a series of districts, affecting the outcome of the election:

Probability II Minnesota Senate

The above formula was then applied where, α is a vector representing the number of Franken votes in a given district; &beta a vector of Coleman votes in a given district and κ a vector containing the number of potentially invalid errors using yesterday's definition and assumption. The variables a and b contain the number of total votes received by each of the two leading candidates; 1,212,431 and 1,212,206 respectively. The probabilistic results are depicted below using data from six previously provided tables:

Rejected List               z       Pr(z)    Ballots   Proj
Anomalies by Precinct    .220910   41.258%    1,391   + 5 Col
Anomalies by County      .015925   49.364%    1,391   +31 Fra
Coleman List v3          .000854   49.659%    4,458   +45 Col
Franken X                .029226   48.834%      781   +15 Fra
Franken Y                .030776   48.772%      804   +63 Fra
Registration Error       .018800   49.250%    1,526   + 4 Fra
Statewide*              2.755361     .293%    6,653     N/A

Today's result varies significantly from yesterday's result[*], which depicted a probability of <1%. The bottom line is that if there are errors, and they can legally be corrected, Coleman could overcome the current deficit of 225 votes.

Now onto the actual litigation proceedings; the MN Supreme Court released three documents today, and MinnPost obtained a fourth filed by the Election Contest Court. I've posted links to these documents below, but I have not had time to review them:

1. Motion of Norm Coleman to Intervene (3-5-09) via [PDF]
2. Affidavit of Charles N. Nauen (3-3-09) via [PDF]
3. Memorandum Regarding Timeliness of Petition (3-3-09) via [PDF]
4. Franken's Motion to Dismiss via [PDF]

Rasmussen Reports just released a new poll detailing the whole MN Senate Situation and the public's response, here are the highlights:

Forty-seven percent (47%) of Minnesota voters now believe Democrat Al Franken has been elected to the U.S. Senate in a race so close that it's been working its way through the state's court system for the last four months.

Thirty-five percent (35%) believe incumbent Republican Senator Norm Coleman will be re-elected, and 18% are not sure in the latest Rasmussen Reports survey of Minnesota voters.

Coleman, who now trails Franken, has proposed that the state vote again because of the closeness of the race, but Minnesota voters are almost evenly divided on his proposal. Forty-six percent (46%) think they should vote again, but 44% disagree. Ten percent (10%) are not sure which is best.

Not surprisingly, 71% of Republicans support a revote, while 69% of Democrats are opposed. Among voters not affiliated with either major party, a revote is favored by 12 points.

Source: Rasmussen Reports

Based upon the results, it appears as though the partisan interviewee responded along partisan lines, while the self described independent voter took an independent position. If you look at the Nov 4th exit polls, it appears as though these self described independents tended to favor Coleman over Franken by about 20%. Having established this potential bias, I think its fair to say that these independent voters present the least biased opinion and they seem to support the notion that Franken won, but that another election would be favorable. In the end however it is not public opinion that will decided the victor, it is the opinion of the three judges presiding over the litigation process.

Update [8:46 PM CT 3/6/2009]: I made the same mistake when computing the probabilities in this article, as I did in the original. The errors have since been corrected; the equation image and table have been updated to reflect these changes.

The fundamental conclusion of the original result still holds as the changes actually improved the overturning probability. The probability that the invalid votes could overturn the current result answers the question of do these inaccuracies matter? The current answer is yes at around 50% for the six calculated lists; the nature of each list does not preclude complete conclusion, as such, these percentages represent the maximum overturning probability.

With a 40% probability of affecting the final outcome, the identified inaccuracies, by both campaigns, deserve to be addressed within the litigation process; which is exactly why the trial has progressed into it's 30th day.

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