This graphic from Nate Silver at fivethirtyeight.com makes a good, simple, case for where the smart money should be targeting a public option compromise with the biggest bang for the buck that will leave most stakeholders with a winning hand.

The level-playing-field (Federal Program, Negotiated Rates) Public Option with an Opt-Out mechanism is exactly where we should be setting our sights.

A Federal Program paying Medicare +5% is problematic for a number of reasons especially in that the markets where the effects of Medicare cost shifting are strongest would be even further disadvantaged by this arrangement, possibly leading to unsustainable systemic breakdowns. (And yes, I recognize that the status quo is leading us toward unsustainable systemic breakdowns.)

Additionally, some markets may indeed see drastic unintended consequenses from a public option, and so the ability to opt-out without a federal shutdown could actually be beneficial (as well as an incentive for the public option to benefit every state). This is a bit counter-intuitive in that this scenario is actually only more likely in locations who are probably the most pro-public option philosophically; while the states who are most certain to depend on a viable public option are the most likely to oppose it on a referendum or a state legislature (ideologically at least).Be that as it may, such a public option really would have a large enough market share to be considered robust, and has a very interesting, very seldom discussed Actuarial advantage over just about any other private health insurance.

Namely, Private insurance plans can only expect to keep their members for a finite number of years. Most of these members are through employer groups whose employees turn over at a fairly consistent rate. This turnover rate means that investing in preventative care today can only pay off in ten or fifteen years if that member is still employed by that firm and insured by the same company. (Of course, often times members leave and come back to the same company - but not enough and as predictably as necessary).

But a public option has a high likelihood of keeping a member for a long time as many of these members will be in lines of work which will not be employment dependent, (some will come in and out of course) but most relavantly, everyone will end up in Medicare!!Because everyone ends up in Medicare, the public option can actually become incentivized by saving future Medicare money by investing in longer-term health and wellness prevention. This is an absolutely critical connect-the-dots exercise.

Having the public option negotiate rates and contracts seperate from Medicare will allow better innovation along these lines (although we should expect the public option to probably base its fee schedule off Medicare as it enters into contract negotiations.)

The other critical piece is that the Individual Mandate needs teeth. The insurance companies were dickheads when they came out with their reports a couple of weeks ago, but they were right on the point about how critical it is that an individual mandate be an actual mandate. Self-selection is just too obvious an insurance problem and with the lengths we are going to make insurance affordable and accessible to everyone, we need to make it unacceptable to choose to go uninsured.

Trailing Digit Distribution Charts

On September 25 & 26, 2009. Nate Silver (fivethirtyeight.com) suggested that we could examine the distribution of trailing digits in the leading two percentages from political candidate/issue polling to verify the veracity of certain pollsters. His first assertion that we might compare this digit distribution to something approching a uniform distribution struck me as off so I decided to apply a more thorough methodology.

First, let me be clear about where these trailing digits come from. A poll from pollster X says candidate A leads candidate B 45-41. We take this poll as one data point and count one 5 and one 1. This poll is saying 45% prefer A, 41% prefer B, and implies the remaining 14% are undecided with a spread of 4% between candidates. We can transform this input to focus on the distribution of the undecided and spread figures.

The distribution of the undecided figure is likely to be different between different types of polls and pollsters themselves, as the way the interview is conducted effects how likely a respondent is to state a preference. Also, pollsters may specialize in types of polling which is more or less likely to have a larger undecided figure.

The distribution of the spread between the leading and trailing candidate is also likely to very from pollster to pollster as some pollsters may be more or less interested in polling close races/issues.

In both cases, however, these distributions should be very smooth. We can work out distributions which approximate the data sets we have. We can then use those distributions to predict the natural distribution of trailing digits.

Using a closely fitting Gamma Distribution with parameters alpha = 3 and beta = 2.5 for the % undecided, and a Gamma Distribution with parameters alpha = 1 and beta = 7 for the % spread I use a Monte Carlo method to develop an expected trailing digit distribution for Strategic Vision:


This assumes each poll has 1200 interviews with an whole number of persons favoring A, B, or undecided. I randomly conduct 2772 polls and count the trailing digits. Then I repeat the process 1000 times and take the mean frequency of each digit. Visually, we see this comport somewhat with the actual distribution observed with Strategic Vision, but with a Chi-squared distribution we see that only 0.011% of pollsters with this undecided/spread distribution would have a trailing digit distribution this strange.

In contrast, when we examine Quinnipiac's undecided/spread distribution and allow the undecided % to be Gamma Distributed with parameters alpha = 3.5 and beta = 5 , and the spread % to be Gamma Distributed with parameters alpha = 1 and beta = 6 we find something much closer.
After applying the same Monte Carlo method we find that 18.022% of pollsters would be expected to be this dissimilar from the predicted distribution, well within the range of reasonably likely events.

Looking back at the Strategic Vision dissimilarities, the thing that jumps out at me is what I take to be the replacement of 6's with 5's and 1's with 0's in the trailing digit. If we modify our methodology to incorrectly round numbers like 45.5% down to 45 instead of up to 46% and 30.5% down to 30% instead of up to 31%. (i.e. in all cases where the percentage rounded to the tenths place ends in 5.5% or 0.5% we incorrectly round down we get the following distribution:

In this scenario, we can expect 12.57% of pollsters with the same undecided/spread distributions to produce actual distributions this dissimilar. Were this the case, we would say that this pollster was using a seriously flawed rounding methodology.

If this is not the case, we have strong evidence of fraud.