Consequentialism -X- (Pareto Efficiency) -X- Deontology

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Let us check the Polity to begin with:

1. N is the set of all individuals in society.

And that which their politics concerns – the state of society.

2. S is the set of all possible information contained within society, so that a set s ∈ 2S (2S being the set of all possible subsets of S) contains all extant information about a particular iteration of society and will be called the state of society. S is an arbitrary topological space.

And the means by which individuals make judgements about that which their politics concerns. Their preferences over the information contained within the state of society.

3. Each individual i ∈ N has a complete and transitive preference relation ≽i defined over a set of preference-information Si ⊂ S such that si ≽ s′i can be read “individual i prefers preference information si at least as much as preference-information s′i”.

Any particular set of preference-information si ⊂ Si can be thought of as the state of society as viewed by individual i. The set of preference-information for individual i is a subset of the information contained within a particular iteration of society, so si ⊂ s ⊂ S.

A particular state of society s is a Pareto efficient if there is no other state of society s′ for which one individual strictly prefers their preference-information s′i ⊂ s′ to that particular state si ⊂ s, and the preference-information s′j ⊂ s′ in the other state s′ is at least as preferred by every other individual j ≠ i.

4. A state s ∈ S is said to be Pareto efficient iff ∄ s′ ∈ 2S & i ∈ N : s′i ≻ si & s′j ≽ sj ∀ j ≠ i ∈ N.

To put it crudely, a particular state of society is Pareto efficient if no individual can be made “better off” without making another individual “worse off”. A dynamic concept which mirrors this is the concept of a Pareto improvement – whereby a change in the state of society leaves everyone at least indifferent, and at least one individual in a preferable situation.

5. A movement between two states of society, s → s′ is called a Pareto improvement iff ∃ i ∈ N : s′i ≻ si & s′j ≽ sj ∀ j ≠ i ∈ N .

Note that this does not imply that s′ is a Pareto efficient state, because the same could potentially be said of a movement s′ → s′′. The state s′ is only a Pareto efficient state if we cannot find yet another state for which the movement to that state is a Pareto improvement. The following Theorem, demonstrates this distinction and gives an alternative definition of Pareto efficiency.

Theorem: A state s ∈ 2S is Pareto efficient iff there is no other state s′ for which the movement s → s′ is a Pareto improvement.

If one adheres to a consequentialist political doctrine (such as classical utilitarianism) rather than a deontological doctrine (such as liberalism) in which action is guided by some categorical imperative other than consequentialism, the guide offered by Pareto improvement is the least controversial, and least politically committal criterion to decision-making one can find. Indeed if we restrict political statements to those which concern the assignation of losses, it is a-political. It makes a value judgement only about who ought gain (whosoever stands to).

Unless one holds a strict deontological doctrine in the style, say, of Robert Nozick’s Anarchy state and Utopia (in which the maintenance of individual freedom is the categorical imperative), or John Rawls’ A Theory of Justice (in which again individual freedom is the primary categorical imperative and the betterment of the “poorest” the second categorical imperative), it is more difficult to argue against implementing some decision which will cause a change of society which all individuals in society will be at worst indifferent to. Than arguing for some decision rule which will induce a change of society which some individual will find less preferable. To the rationalisitic economist it seems almost petty, certainly irrational to argue against this criterion, like those individuals who demand “fairness” in the famous “dictator” experiment rather than accept someone else becoming “better off”, and themselves no “worse off”.

Arrow’s Theorem on Dictatorship. Thought of the Day 49.0

Arrow_s+Impossibility+Theorem

Let A be a set of alternatives, and J be a set of individuals.

P(A) is a set of preference relations on A. These are usually taken to be weak orders (transitive, connected and irreflexive).

P(A)J is the set of profiles or ballots, which assign a preference relation on the alternatives of each individual – a ‘vote’.

A social welfare function is a map

σ: P(A)J → P(A)

Such a map produces a single ranking on alternatives – a social choice – from a profile.

Two conditions are standardly considered on such functions:

– Independence of Irrelevant Alternatives (IIA). The social decision on the relative preference between two alternatives a, b depends only on the individual preferences between these alternatives. It is independent of their rankings with respect to other alternatives.

– The Pareto or Uniformity Principle (P). If every individual prefers a to b, then so should the social welfare function.

So, what then is Arrow’s Theorem?

If |A| > 2 and J is finite, then any social welfare function satisfying IIA and P is a dictatorship, i.e. for some individual i ∈ J ∀ profiles p ∈ P(A)J and alternatives a, b ∈ A:

a σ(p) b ⇐⇒ api b

Thus, the social choice function, under these very plausible assumptions, simply copies the choices of one fixed individual – the dictator.

A closely related result is the Gibbard-Satterthwaite theorem on voting systems.

If |A| > 2 and J is finite, then any voting system

v: P(A)J → A

which is non-manipulable is a dictatorship.

For an area of study to become a recognized eld, or even a recognized subfield, two things are required: It must be seen to have coherence, and it must be seen to have depth. The former often comes gradually, but the latter can arise in a single flash of brilliance. . . . With social choice theory, there is little doubt as to the seminal result that made it a recognized field of study: Arrow’s impossibility theorem.

Political Ideology Chart

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It displays anarchism (lower end) and authoritarianism (higher end) as the extremes of another (vertical) axis as a social measure while left-right is the horizontal axis which is an economic measure.

Anarchism is about self-governance, having as little hierarchy as possible. As you go to the left, the means of production are distrubuted more equally; and as you go to the right, individuals and corporations own more of the means of production and accumulate capital.

On the upper left you have an authoritarian state, distributing the means of production to the people as equally as possible; on the lower left you have the collectives, getting together voluntarily utilizing their local means of production and sharing the products; on the lower right you have anarchocapitalists, with no state, tax or public service, everything operated by private companies in a completely free and global market; and finally on the top right you both have powerful state and corporations (pretty much all the countries).

But after all, these terms change meanings through history and different cultures. Under unrestrained capitalism the accumulation of wealth both creates monopolies and more importantly political influence. So that influences state interference and civil liberties also. It also aspires for infinite growth which leads to the depletion of natural resources which is another diminishing fact for the quality of living for the people. At that point it favors conservatism rather than progressive scientific thinking. Under collective anarchism, since it’s localized, it is quite difficult to create global catastrophes, and this is why in today’s world, the terms anarchism and capitalism seems as opposite.

Is the Hierarchical Society Cardinal?

Even the question posed has a stink of the inhuman, or un-human, though it is evident that in theory we might try and flatten such hierarchies, the same never holds true in practice. Although such hierarchies might be held on to surreptitiously, the tendency to be resilient is never really ruled out in matters as sensitive as these, which make us prone to getting branded as fundamentalists or fanatics, or anything which has semblance to the right-wing ideology. So, in a nutshell, hierarchies in the Social are indeed emanating from the right-wing, or are at least given to sway in their descriptions and prescriptions.

So, are these hierarchies important? Well, the answer at first go is a strict ‘no’. But, let us deliberate upon. One way is to look upon hierarchy as dominant, and the other is identity when there is an absence of hierarchies. Now, those that belong to the first camp would imply reciprocity as enabling social order. Reciprocity is a relationship that exists one-to-one, one-to-many and many-to-one as regards the first camp, while one and the many merge into one another as regards the second camp. In the first camp, reciprocity is built up on adherence, while in the second, it is more and more symbiotic. The existing of social strata could advocate the existence of micro-cultural forms characterised by the features that lead to the formation of such strata in the first place and could include notions like religiosity, power (both muscle and economic), cultural and intellectual/ideological. On the flip side, such notions are tolerant towards multiculturalism or pluralism. Dominance becomes a nested approach, while becoming-identity is a web-like structure with nodes of individuals or clusters of societies that interact on a horizontal level, or to put it more politically, act on a democratic level, in theory at least, to say the least. Disturbance in this net is knotted into a nest, where dominance takes over the democratic structure and subsequently forcing the second camp to be evacuated onto the first one. Now here is where the catch lies. From netted to a nested structure would mean classification, and it is classification that gets conceptual authority, thus in a hugely ironical manner ameliorating the potential of conflicts due to centralised authoritarian structure. This is its use value. Hierarchies try to make sense out of the apparent relationships between things with the caveat that orientations that determine those relations are just looming round the corner.

In hierarchical societies there are domains of individuals, clusters, micro-cultures or societies that are instances of isolated-ness from each other, whereas in non-hierarchical societies these domains tendentially overlap into one another, or even across one another making the very study of latter kind of studies difficult in intent. Other use value would lie in mapping domains become easier in dominance or stratified societies as compared with in non-hierarchical societies.

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