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Los Angeles Measure A probabilities of passing

Introduction

Measure A would increase a Los Angeles County sales tax from 0.25% to 0.50%. It would raise $1 billion annually for shelters and housing services for the homeless. Los Angeles County has a homeless population of over 75,000 or about 40% of California's total homeless population.

Measure A, at the Los Angeles County level, would very much supplement Proposition 1, at the State level, that passed in March. However, Measure A packs quite a fiscal punch, as it would raise $1 billion annually. By comparison Proposition 1 raises a one time $6.4 billion through bond issuance. So, over a 7 year period Measure A at the LA County level would have raised more than Proposition 1 at the Statewide level.

The poll was conducted between September 25 and October 1 by the UC Berkeley Institute of Governmental Studies.

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Caveat

The statistical approach I am using has limitations. It is not a crystal ball. It tells you the voter preferences by October 1. It does not tell you how voters will actually vote by November 5. Also polls may have structural flaws associated with inaccuracies whereby their weighting of the various voters' categories is different than the actual one by November 5.

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Converting polls into probabilities

The first step is to take the Undecided out of the sample. So, we are left with only likely voters who poll Yes or No . When we do that the polls are very close to 60%/40% in support of Measure A.

The next step consists in calculating the variance and standard deviation of such a poll. Focusing on the Yes for Measure A, the calculations are as follows:

Variance & Standard Deviation:

(59.8%(1 - 59.8%))/SQRT(745) = 0.03%

745 is the adjusted sample size once we take out the 18% Undecided

Standard deviation = square root of Variance = 1.8%

Error Margin and 95% Confidence Interval:

Error Margin x 1.96 Standard Deviation: 1.8% x 1.96 = 3.5%

95% Confidence Interval maximum value or 97.5th percentile:

59.8% + 3.5% = 63.3%

95% Confidence Interval minimum value or 2.5th percentile:

59.8% - 3.5% = 56.2%

The graph below visualizes this 95% Confidence Interval.

The 95% represents the area under the Bell curve (total area = 100%) in between the two vertical dashed red lines. The 95% represents the probability that the accurate value of this poll is between 56.2% and 63.3%. This captures the uncertainty associated with small sample errors.

Final step converting the polls into probabilities

We need to calculate the distance between Measure A Yes polls at 59.8% and the 50% needed to win. And, we measure this distance in number of Standard Deviations.

(59.8%- 50.0%)/1.8% = 5.4 Standard Deviations.

Using the NORMSDIST() function in Excel, we derive that 5.4 Standard Deviation above the 50% threshold to win is associated with a 100% probability of winning.

Below we visualize this 100% probability by looking at a probability density function (PDF) graph. The 100% represents the area under the Bell curve to the left of the vertical red dashed line.

We can also visualize this 100% probability by looking at a cumulative distribution function (CDF) graph. And, now this probability is captured on the Y-axis.

Whether we focus on the PDF or the CDF graph, we can see that at over 5 standard deviations over the 50% threshold to pass Measure A, statistically, appears most likely to pass.

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Let's explore what it would take to defeat Measure A

This poll had 18% Undecided. We know that Measure A among the Decided Tleads by close to 60%/40%. So, by how much do the Nos need to to potentially lead among the 18% Undecided to turn this thing around?

Among the Decided, the Yes lead 49% to 33%, or by 16%. To even things out, the Nos need to lead by the same 16% among the Undecided. Thus, the Nos need to lead by 17% to 1% among the 18% Undecided. When you prorate the 17%/1% among the 18% Undecided, the Nos have to lead by close to 94%/6% among the Undecided to potentially win.

Below we visualize the interesting contrast between the Yes lead of close to 60%/40% among the Decided vs the necessary lead the Nos need among the Undecided at close to 94%/6%.

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What is the probability that Opposition can swing the Undecided?

We can use the same framework to figure out the prospective 95% Confidence Interval for the Nos among the Undecided.

The table above focuses solely on the sample of the Undecided (163). We assume that the starting poll among the Undecided is similar to the one among the Decided at 40.2%.

Given that the sample is small, the Standard Deviation is much higher at 3.8%. The Error Margin is 7.5%. And, the 95% Confidence Interval ranges from 32.7% to 47.8%.

We visualize this 95% Confidence Interval below.

If we assume that the starting poll for the Undecided is 40.2% (same as for Decided), the above indicates that there is less than a 2.5% probability that the No poll among Undecided would be greater than 47.8%. That's because both tails of a 95% Confidence Interval represent only 2.5% of the surface under the Bell Curve.

But, the Nos have to reach a prospective poll of over 94% among the Undecided to potentially win. So, the Nos' probabilities of reaching this much higher threshold is very close to 0.0%

We can calculate this probability using 1 - NORMSDIST(14.1). This is because 94.4% is 14.1 Standard Deviations above the starting poll of 40.2%. And, the resulting probability is very close to 0.0%.

As reviewed, Measure A appears most likely to pass. If not for the mentioned caveat (standard for all polls), we would say Measure A passing is a sure thing.

THE END

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