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In political science, accountability is the measure of perceived political power held by a constituency over its representatives.

Accountability in government is often touted as the great accomplishment of the European political tradition. In fact, it is Communism which most truly achieves this ideal by uniting the very truth of government with the body of the working population. Accountability in a capitalist society is limited to the bourgeoisie, which pursues its own ends in the corrupted apparatus of the state; only under Communism are the people truly free.

Theory of Accountability

Accountability necessarily decreases as the size of the population rises; either the number of representatives remains fixed, diluting the influence of an individual member of the representative's constituency, or it increases, diminishing the influence of each representative on the total disbursement of power. This argument, called the Razor of Damocles, can be made arbitrarily rigorous: consider the represented-by mapping e, a surjection e from the population set P into the representative set R. Given a representative r in R, there exists a constituency set C which is the pre-image of the singleton r under e. An accountability-assignment A assigns accountability values v to members p of the population P such that the sum s of v for all p in each C for an arbitrary r is 1. We can assign a partial order o to such A, allowing P to range freely, such that A1 precedes A2 if its domain D2 is a subset of D1 and v1 precedes v2 for each p in D1; note that inequality i here mandates a strict inequality j of domains D, i.e. an increase in population P from D2 to D1. Assuming finite sets R and C for each r in finite set R permits a calculation of the mean m of v for each p over the set C for each representative r; that this decreases by a population increase I is given, Q.E.D. We are indebted for the idea of this proof to Bleck, W., and Cambwell, Q., who wished to remain anonymous.

Non-Damoclitian Accountability Theory

In the 1700s, mathematicians began to investigate the necessity of the assumptions in the proof above. This "fifth-axiom" moment led to philosophical questioning of the naturality of classicalist accountability theory, which emboldened a young Karl Marx; but we constrain ourselves here to the dull lustre of our mathematical accountability.

The key idea is to imagine a game of hop-scotch. Chalk out ten or so regions on a manifold, by-and-large in a linear progression but always with several diagonal pairs interspersed throughout the sequence; this is the core of the proof. Imagine a school-girl playing the game. She throws her stone; it lands in the correct square; she advances to the end of the hop-scotch, skipping the stoned region, but she has not reached the end of the game. Instead, she turns, advances to the beginning, pausing only to retrieve her stone. She then throws her stone to the next region in the sequence, ad infinitum, but ad que infinitum? When she places her stone in a diagonal pair, it nonetheless remains possible to progress forward without jumping over an entire row --- so the removed region must be discontinuous with the ordinary number line! This is sublime nature of the diagonal pair, which Cantor recognized in his celebrated proof. The paired regions can be imagined as a second sequence through the manifold, but even the youngest of girls can easily incorporate this sequence into that of the primary progression --- but regions must be dropped!

This demonstrates that these hop-scotch squares must exist at a higher rank of infinity than those of populations; it becomes impossible to compute means of assignments over them; in short, they have become unaccountable.