One of the many odd things about the whole IQ measurement business is that significantly less than 50% of any large human population is in any practical sense of below average intelligence -- so when Gallup recently announced that Mr. Obama's popularity had soared to achieve a 50% approval rating, I started to wonder just how that miracle had been achieved.

Gallup generally tries to run an honest business -- and their predictions for 2012 were close to spot on if you estimate the vote in GOP no-go areas like those in Ohio and Pennsylvania where Mr. Obama's people recorded roughly 100% of eligible voters as having voted democrat, at average rates for demographically similar, but smaller and GOP auditable, precincts elsewhere.

Unfortunately Gallup's efforts at running a clean survey led them to predict a Romney victory and that, in turn, left them to do some serious soul searching when Mr. Obama appeared to win instead.

In response they introduced at least two types of change: a reweighting of the assumed land-line to cell phone mix to 50:50 together with the adoption of random digit dialing -- and it is the consequences of these changes that account, I think, for that 50% approval rating.

Please be aware in reading this discussion, however, that national opinion polling is a very difficult business with serious hidden complexities throughout and therefore, without longer-term access to real data including full call logs and the detailed weightings used in sampling and/or analysis, my thoughts on this issue are, and must remain, purely speculative.

What random digit dialing generally means is that survey calls are placed to phone numbers selected from lists compiled by taking all possible numbers for each area code and exchange in the United States, (optionally) dropping numbers known not to be registered to individuals, and ignoring numbers that turn out to be unused or disconnected when the call-out process encounters them.

The most basic requirement in using sampling to estimate population ratios is that every member of the target population must have an equal chance of being drawn as part of the sample, and all, or very nearly all, of the sampled must provide the required information.

It is easy to get close enough to this ideal to get reasonable results if you have a truckload of bottlecaps and want to estimate what proportion say "Coke" on them -- because the things picked out of the truck as samples are unambiguously identifiable as either bottlecaps or something else and, equally unambiguously, either say, or don't say, "Coke" on them.

Unfortunately, that simplicity does not exist in political preference estimation where a telephone interviewer has no way to know whether the person at the other end really is an eligible voter -- instead of a teenager, illegal immigrant, career criminal, or visitor from Alpha Centauri. Worse, some demographic groups (e.g. older women) often enjoy answering surveys, some (e.g. younger conservative males) generally don't; some (e.g. the urban uneducated and politically committed) may be more likely than most to complete a political survey if you can get them to answer a phone, but are also much less likely than most to be either introspective or truthful in their responses -- and, of course, you don't have to listen to a lot of calls to find interviewers completing interviews through their intuitive understanding of responses from non-English speakers, the nearly deaf (who often can't follow the questions), and the usual grunters, criers, screamers, and mid-course hangers-up.

As a result polling companies put a lot of effort into correcting the resulting distortions in the sample by weighting responses according to demographic and other criteria -- in reports on Canadian health care satisfaction surveys, for example, a teenager's "okay, I guess" is usually given many times the weight accorded a senior citizen's litany of complaints.

In the real world of political polling the most important consequence of random digit dialing is that the survey universe is the set of working personal phones -- not the set of all eligible voters. The impact of the 50:50 assumption (which should say that the sample provides no applicable information) is less clear because good numbers are hard to come by, but almost everyone agrees that there are now more mobile phones than fixed ones and therefore that the 50:50 assumption, if enforced on the data, would distort the result toward over weighting responses from fixed phone users.

Thus the combination of random digit dialing with a 50:50 assumption produces three immediate consequences:

1. First, since Gallup (and other) survey personnel are instructed to ask for an adult if a minor answers the phone, the mother in families in which the adults and teens have personal cell phones but the family also has a shared home phone is more than three times as likely to be selected into the sample (and more than twice as likely to complete the survey) as someone answering only one personal phone;
2. Second, random-digit dialing disconnects sampling from the paying subscriber lists which used to act as proxies for voter lists. As a result, polling companies using this approach are seeing results shift toward a younger, more immigrant intensive, population as people who aren't eligible voters claim eligibility for reasons including wanting their voices heard (mainly teenagers); not wanting to say they are illegals; not wanting to offend against what they imagine is an official information demand (mainly legal immigrants); or simply because they want to please the caller.
3. There are, in addition, some emergent problems, prominent among which are the likelihood that two randomly selected seven digit numbers within the same area code will reach the same respondent, and the fact that cell-phone accounts are increasingly likely to have area codes unrelated to the holder's current primary address.

The 14 million or so "lifeline" (Obamaphone) holders tend to be among the least knowledgeable (but most committed) of Democrats -- making them on the one hand somewhat more likely to be reachable and willing to respond than the average for cell phone users, but also both less willing and less able than average to tell an interviewer who has just read them a list of five or more choices and recorded their choice, either what they picked or why.

All three consequences tend, on average, to bias the sample, and thus the survey results, toward Democrats in general and Mr. Obama in particular -- and this makes sense, of course, because the point of making the adjustments at all was to more closely match polling results to the official vote counts from the 2012 presidential and senate elections.

And while the resulting tilt probably explains how Mr. Obama can claim a 50% approval rating from Gallup while apparently doing everything he can to destroy the country from within, it also raises a much bigger question because the theory says that these adjustments should have weakened, not strengthened, the poll's predictive value -- a claim, let me repeat, based on inadequate information about Gallup's actual data and processes and therefore about which I might change my opinion if given better information.

Since we know that the sample sizes were adequate; that the changes were intended to produce a closer match between Gallup's predictions and the 2012 electoral outcome; that this worked; and that the changes made appear to be contra-indicated by sampling theory, we are left with three options: either the theory is wrong, a huge opinion shift took place during the last few hours before voting closed, or the official electoral result did not match the actual vote.

The Snopes attempt at fisking fraud allegations to the contrary, I think that choice is a no brainer -- because Gallup's people knew what they were doing in 2012, and the theory isn't wrong.