Comparison of Voter Power in the 2008 Presidential Election using

Three Distinct Methods for Electoral Vote AllocationZubin Huang, Michael Landau,

Stephen Podowitz

Problem• In the United States, presidents are indirectly elected

through an Electoral College system.• Electoral College system distorts this equality and

introduces additional variables that cause different voting power.

• We determined the extent to which the Electoral College system caused voting power to vary between the individuals of the various states for the 2008 election.

• We also use these models to compare both the absolute values of and the disparities between voting powers of individuals employing the traditional, national popular vote, and district methods.

Formulation• P(Change US election | voter votes in state x) = P(change election in

state x) * P(state x changes the whole US election)

•

• P(i, k) = pi*P(i-1, k-vi) + (1-pi)*P(i-1,k)– P(i, k) : the probability of Obama having k electoral votes after

counting i states. – pi: the probability Obama wins state i, – Vi: the number of electoral votes of state i.

• A beta distribution was used to assign the probabilities pi, based on simulated polling data of a 600 person sampling from the voter population

( /2) ( /2)(Swing within State) (1 )/ 2

n nnP p p

n

Data

• The vote counts by state and county for the 2008 presidential election were retrieved from NYTimes.com on November 17, 2008.

• Voting population and probabilities were calculated only from votes cast for Obama and McCain.

• For counties falling within more than one district, votes were proportioned by the percentage of votes cast in the concurrent congressional races within these counties

State-level Scenario Analysis

• States that supported Obama were found to have much higher probabilities of changing the national election.

• DC was more likely to have changed the outcome of the 2008 election than TX.

State Scenario Sensitivity Analysis

• Sensitivity analysis for CA (extreme democrat), NC (toss-up state) and WY (extreme republican). These results indicate that for moderate states and states that back the losing candidate, variations in electoral votes do not significantly change the probabilities.

Individual voting powers

• CA was determined to have the smallest and MO the largest voting power of all states. • Of the six delegations with the smallest voting power, five—CA, NY, IL, MA, and MD—had

relatively large voter populations, and all supported Obama with probabilities of 0.62, 0.63, 0.63, 0.63, and 0.63, respectively.

• The remaining delegation, DC, had a small voter population of ~225,000, but had a 0.93 probability of supporting Obama.

• MO, NC, and IN had the largest voting power and the probabilities of supporting Obama closests to 0.5—0.499, 0.501, and 0.505.

Voting power as a function of voter population (n)

• Disparity between the voting powers of the two states linearly increases with increasing population size and is proportional to the difference between the probabilities. The large disparity in voting power between states with similar voting probability, such as DE vs. IL and NM vs. NJ, arises from this significant difference in P(k=n/2) for large n.

1.¥ 106 2.¥ 106 3.¥ 106 4.¥ 106 5.¥106

10- 1 262 901

10- 1 010 320

10- 757 739

10- 505 158

10- 252 577

Voting power as a function of voting probability (p) with n held constant

• There is a parabolic relationship between P(k=n/2) and p, so the second partial derivative is constant over the entire range of p. Because an absolute maxima in P(k=n/2) occurs at p = 0.5, the disparity between two populations with different n increases with increasing p over 0.5. In other words, the effect of variation in state size on disparities in voting power is exacerbated for the case of states with extreme voting outcomes.

0.4 0.5 0.6 0.7 0.8 0.9

10- 133 801

10- 107 040

10- 80 279

10- 53 518

10- 26 757

District and statewide voting powers (P(k=n/2)) for NC, NE, ME, and TX.

• Although voting in NC resulted in a state voting power greater than all districts but one and one district in NE was well above the voting power statewide, the calculated probability lies within the range of district probabilities.

• For ME and TX, the calculated probabilities fall outside the range of district probabilities, and the average p for districts in TX is well below calculated value.

• For this spread of states, the calculated voting probabilities were found to be reasonable values to be obtained on the district level for states with higher voting power, but too extreme for those states with low power.

• Therefore, the disparity in voting power between voting-pools can never realistically be as extreme for the district method as it may be for the current state method.

State State Voting

Power

(P(k=n/2))

Average

District Size

(n)

Calculated

Voting

Probability

(pcalc)

Actual District Voting

Probability (p or 1-p)

Range Average

NC 9.429 × 10-14 325634 0.5060 0.5033 – 0.6616 0.5605

NE 3.982 × 10-4049 259311 0.6316 0.5497 – 0.6995 0.5844

ME 3.723 × 10-4827 358837 0.6225 0.5716 – 0.6010 0.5863

TX 5.299 × 10-24532 249654 0.8016 0.5036 – 0.7697 0.5952

Conclusion• The district method was found to constrain the minimum voting

power of significant minorities within a district to a larger extent than the national popular vote and traditional methods, while maintaining a lower level of disparity than the traditional method.

• The probabilities of the outcome in a state changing the election result under the traditional method were found to be negligible compared to the probabilities of an individual voter within a state changing the outcome of the state. However, the voting population and probability had an inverse effect on the two levels of probability for states strongly favoring Obama.

• Voting power was found to be dependent on both voting population and voting probability, and therefore limitations on the disparity of these two parameters between voting-pools will limit voting power disparities between individuals in these pools. The district method allows for the greatest possibility of limiting both and requires no significant policy changes on the federal level.