I have been often frustrated, upset, angry and humiliated at my inability to “win” debates, in which I was certain I had all the facts on my side and have constructed an unassailable logical chain. Despite my best efforts I was unable to convince the opposing side that their position is indefensible.

Without realizing, I was assuming that this inability was due to a fault of mine: I was either not as well-informed as I should have been, or I was not articulate enough in making my case, or I was not clever enough in rebutting the false arguments made by the opposition.

In some cases, I was undoubtedly at fault. In fact, I now consider some of the positions that I have advocated at those times to be wrong. But, be that as it may, one of the sides of the debate was wrong, and whether it was me or the opposition, neither side was convinced as the debate ended. If either side did eventually come to change their position, it was long afterwards, with much more reflection, fact-gathering and debate.

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Having discussed briefly his rather convincing concept of Ideal Democracy, Dahl quickly moves on to what he calls “Actual Democratic Systems,” being mainly modern Western-style government systems (WSGSs), but including also the Athenian system, both of which he presents as being approximations to the ideal democracy.

The remainder of the book usually makes no clear distinction between an “Ideal Democracy” and “Actual Democratic Systems”. For example, the remainder of chapter 2 – the sections “The growth of political equality” (pp. 22-24), and “A brief sketch of movements toward political equality” (pp. 25-29) – deals mainly with the existence of WSGS institutions and the widening of voting rights, implying that those are equivalent to, or at least direct indicators of, political equality. No reference to the standard laid out in the description of the Ideal Democracy is made. Similarly, chapter 4, “A respectable role for emotions”, makes frequent references to events associated with the formation of WSGSs as we know them today in order to make arguments about the processes leading to political equality.

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A review of the facts so far: Americans are not satisfied with Congress, they think most congresspeople are corrupt and serve special interests, but are reasonably satisfied with their own representatives and believe they are not corrupt (at least not as corrupt) and serve the people (at least to some extent).

Clearly, the public’s sentiments cannot be an accurate perception of reality: If each district sends an honest representative who is devoted to serving the people, then how can the majority of congresspeople be corrupt? The public either judges most representatives too harshly, or is deluded regarding their own representatives.

The source of the contradiction may be in the different ways in which the people gather information about Congress as a whole and about their own representatives.

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In a previous post I noted that the long term trend of satisfaction with U.S. Congress shows consistently lower satisfaction levels for Congress than for the U.S. Supreme Court and President. In fact, the last year in which Congress enjoyed a rating of “a great deal” or “quite a lot” of satisfaction by more than 30% of the population in the Gallup yearly survey was 1988.

I stated that the fact that incumbency rates of this unpopular body are extremely high (visualized in this chart) contradicts accepted democratic doctrine (which implies that through frequent elections the public can ensure that Congress functions in accordance with the voters’ sentiments). I further stated that the reason for the high incumbency rates is that much as the voters are unhappy with the incumbents they have no reasonable credible alternative candidates – since “reasonable” excludes the candidate of the other major party, while “credible” excludes all minor party candidates.

In a comment, Harald Korneliussen pointed out that lack of alternatives may not be the reason for re-election of incumbents. Voters have no way to replace Congress as a whole, but rather they have only the option of replacing the representatives in their own districts. It could be that voters are unhappy with Congress as a whole, but are quite happy with their own representatives.

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It is often implied, although usually not explicitly said, that debate is like chess: if you gather all the facts, and get your logic straight, then your position will prevail – i.e., you will convince your audience, or at least any member of the audience who does not have a strong inherent bias.

It is supposedly especially so when dealing with an elite, and therefore, rational audience, e.g., scientists or judges. These audiences are less susceptible to rhetorical manipulation and general stupidity. There are a few celebrated cases of supposed failure of elite rationality, but those cases are considered rare enough to merit celebration: for example, the U.S. supreme court failing to see the obvious moral failures of slavery, and the astronomers of 17th century Europe failing to see the truth of Galileo’s heliocentric theory.

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I have just found a short article of Killeen that appears to be a rejoinder to comments on his original p-rep paper. Unfortunately, I have not been able to find the comments to which Killeen is responding, but it appears, from the rejoinder (Error and Correction section), that the fundamental error that I referred to has been pointed out in one of the comments, Doros and Geier. It also seems that another comment by Macdonald pointed out that Killeen’s claim that “the probability of replication” can be calculated without knowing the unknown parameter of the distribution cannot be true.

Somehow, p-rep survived these issues. Superficially, this seems incredible. The entire analysis and rationale given by Killeen for p-rep in his original paper rest on an argument that was discovered to be wrong, and yet the ideas presented by that paper are still considered worth discussing, and even gain official support by the publishing establishment.

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As promised, I have now spent some time reading the first few pages of Peter Killeen’s paper “An Alternative to Null-Hypothesis Significance Tests“. It turns out that Killeen really is utterly and honestly mistaken about his proposed statistic, the p-rep. His entire analysis is wrong because of a relatively simple mathematical error, that any statistician worth his salt could fish out in a few minutes.

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September 14, 2007

I have recently become aware, through a couple of posts in the Cognitive Daily blog (1, 2) of the “p-rep statistic”, which is presented by its inventor, Peter Killeen of the department of Psychology at Arizona State University, in his paper “An Alternative to Null-Hypothesis Significance Tests“, as follows:

The statistic prep estimates the probability of replicating an effect. It captures traditional publication criteria for signal-to-noise ratio, while avoiding parametric inference and the resulting Bayesian dilemma. In concert with effect size and replication intervals, prep provides all of the information now used in evaluating research, while avoiding many of the pitfalls of traditional statistical inference.

The author of the Cognitive Daily blog entries, Dave Munger, describes p-rep as follows:

Very roughly, a prep gives an approximation of the probability that a particular result, repeated on a new sample, would be observed again.


This [prep = .953] means, roughly, that we’re about 95 percent certain that repeating this experiment will give the same results,

along with other comments to the same effect.

I intend to read Killeen’s paper, but I have not done so yet. However, without any hesitation I can already say that Munger’s understanding of what p-rep means is utterly wrong. I’ll excercise some prudence by reserving final judgement on Killeen’s position until after I have read his paper, but it certainly appears that Killeen is wrong as well, or, at the very least, misleading the readers of his abstract.

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Dahl’s description of the Ideal Democracy includes 5 conditions which are fulfilled by a society in which people are politically equal. He seems to consider these conditions to be both necessary and sufficient:

  1. Effective participation
  2. Equality in voting
  3. Gaining enlighten understanding
  4. Final control of the agenda
  5. Inclusion

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The problem with elections

September 6, 2007

This is an essay I originally wrote in the early months of 2006.

A Democratic Alternative to Elections

Legislative bodies are selected through elections in all modern democratic countries. In view of this rule, to which there is not even a single exception, one might presume that elections are the only democratic method to select a legislative assembly. Such a presumption would be wrong. There is another democratic method to select legislators, a method that was used widely in the past (and was in fact considered more democratic than elections), but is almost completely forgotten today.

The alternative method is called sortition [1]. Sortition is the method of selecting the legislators by drawing lots among all the citizens. Those citizens whose names are drawn serve as legislators for a fixed period, as is the common practice with elected legislators. [2]

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