Price elasticity of the consumption of gasoline

Data: Gasoline price, household count and median household income (Table H-5), consumption of gasoline

Update (Sept 1st, 2008): image updated to show 2007 data.
Update (Sept 10th, 2009): image updated to show 2008 data.
Update (Nov 2nd, 2010): image updated to show 2009 data.

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The urbanization of the United States in the 20th century

Data sources Total and rural population: The Statistical Abstract of the United States, 2008, Historical Statistics; Farm population: The Statistical Abstract of the United States, 1925, 1950, 1974 and 1985.

Mean square error of a maximum likelihood estimate is not monotonic in sample size

The IMS Bulletin is usually not a technical publication. It usually carries announcements about upcoming conferences, obituaries, stories about award winners, job ads and columns.

The latest issue of the IMS Bulletin, however, has an unusual item on page 4 in which Ning-Zhong Shi of the School of Mathematics and Statistics, Northeast Normal University, P.R. China lays out “A conjecture on Maximum Likelihood Estimation”. Shi conjectures that the MLE has the finite sample property of having expected squared-error monotonically decreasing in the number of samples n, i.e., MSE( θ_n+1 ) ≤ MSE( θ_n ), where θ_n is the MLE calculated with n i.i.d. samples, and MSE( θ_n ) = E [ (θ_n − θ)² ].

This is a rather bold conjecture, since there is very little established regarding finite sample properties of MLEs. Shi notes that the conjecture is true in the special case in which the MLE is a mean of a sample of i.i.d. variables – such as when the variables are normal or Bernoulli variables parameterized by the unknown mean. It seems that despite applying the qualifier “under some regularity conditions”, Shi expects the result to hold on a much wider set of cases.

He is, of course, wrong.

Plutoctomy

Economic equality may not be a necessary condition for a well-functioning democracy. In an eklogecracy, however, an economic advantage translates to a political advantage. While there are other attributes that confer political advantages in an eklogecracy (this is probably true to some extent in any system of government), large economic advantages are among the most effective ways to gain political power in an elections driven system.

Various devices have been proposed and implemented in an attempt to reduce the ways in which economic advantages can be translated to political power. The most widely adopted device is probably anti-bribery laws. Other, less universally accepted devices are various campaign finance rules. Undoubtedly, those devices have some effect in the intended direction, although, clearly, these devices are far from eliminating the advantages of wealth. It is also clear that eliminating those advantages altogether, or even diminishing them significantly goes against the intrinsic characteristics of eklogecracy and is therefore an unlikely prospect.

Nevertheless, experimentation with additional devices for diminishing the political power of wealth seems desirable. One possible type of devices involves conditioning the assumption of powerful government positions on a renunciation of wealth – a concept which may be termed “plutoctomy”. Under this rule, people running for powerful positions in government, or accepting nominations to such positions, agree in advance that in case they do win the position they will, from that point on and for the rest of their lives, limit their standard of living (as measured by, say, total yearly expenses, including gifts) to a pre-set level (e.g., no more than twice the median level among the citizens).

Delegation and rewards

In a previous comment I discussed the possible types of rewards that may collected by a re-elected delegate. These are the possible rewards that, according to the rewards-based theory of electoral delegation, may be motivating a delegate to be responsive to the interests of the electorate, by having the prospect of re-election available to those delegates whom the public perceives as having acted according to its wishes.

The notion that rewards are an effective way to motivate delegate responsiveness (of which, the rewards-based theory of electoral delegation is a special case) rests on the assumption that citizens can make accurate assessments of the quality of service rendered by delegates. This assumption is unrealistic in many cases – in particular, relying solely on reports in mass media seems like a very shaky foundation for forming an informed opinion on the performance of delegates. Nevertheless, it is interesting to examine what rewards-based mechanisms would be effective motivating factors in those cases where adequate assessment of performance of delegates is achievable.