Political equality in a large group

This post is aimed at being the first part in a long-delayed “attempt to embark on” “a methodical analysis of the set of possibilities for achieving political equality”.

Part 1: Optimal decision-making, group rationality

… in which it is argued that groups, in an ideal setting, can achieve rational decisions. Group decision making constrained by practical circumstances should therefore be designed so as to produce decisions that approximate the decisions that would have been made under ideal conditions.

It is sometimes asserted that groups cannot form good policy. When such notions are expressed by the less educated, they are are attributed to the authoritarian sentiments of the unsophisticated. When such ideas are proposed by the educated, they are considered evidence of hard-headed realism. Elite speakers often mention Arrow’s “impossibility theorem” (what Arrow called the ‘General Possibility Theorem’) and claim that it “shows” that group rationality is impossible.

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Effective U.S. federal tax rate vs. income

The congressional budget office provides data about the distribution of the federal tax burden (including income tax, social security tax, excise tax, and corporate income tax allocated to households according to their capital income) among the different income groups. The chart below shows the 2005 distribution. The area of the entire chart represents the total household income in 2005 ($9.7 trillion).

The chart is divided by solid lines into 5 vertical bars, corresponding to the five household income quintiles, sorted in order of increasing household income from left to right. The bars’ widths correspond to the total income of the quintile (i.e., income per household in the group times the number of households in the group). The top income quintile is split with a dotted vertical line into the two groups – the top 1% on the right and the rest of the top quintile (percentiles 80 to 99) on the left. Those subgroups within the top quintile are broken down further into the following percentile brackets (not marked with vertical lines): [80-90], [90-95], [95-99], [99-99.5], [99.5-99.9], [99.9-99.99], and [99.99-100].

Each bar has a shaded portion corresponding to the share of the income group’s income which is collected as federal taxes. Thus the total shaded area corresponds to the federal tax total ($2 trillion = 20.5% of $9.7 trillion).

The tax rates increase from 4.3% for the bottom quintile to 32.1% for the [99.9-99.9] percentile bracket, before dipping slightly to 31.5% for the top hundredth of percentile.