Steve Watson

Institutions

September 19, 2015 – 9:16 pm

A class of ensembles can be defined for which the EX includes the acceptance of a norm formation. Amongst the subclasses of this we shall seek to define a class of ‘institutions’ that is suitable to play the theoretical role assigned to institutions in HLSTs (but without assuming that those theoretical roles in any particular HLST are well-defined or reflective of sociological reality.) In sociological theories institutions are generally reckoned to be significant features of a society, and there seems to be some primitive notion that underlies the use of the term, but as is often the case the precise definitions offered cover a range of related possibilities. The Stanford Encyclopedia of Philosophy (Miller, S. 2011, s.v. ‘Social Institutions’, ¶1) provides a reasonable overview of the issues and begins by referring to a pair of representative definitions. The first by J. Turner (1997, The Institutional Order, New York: Longman, p. 6): “a complex of positions, roles, norms and values lodged in particular types of social structures and organising relatively stable patterns of human activity with respect to fundamental problems in producing life-sustaining resources, in reproducing individuals, and in sustaining viable societal structures within a given environment.” And the second by Rom Harré (1979, Social Being, Oxford: Blackwell, p. 98): “An institution was defined as an interlocking double-structure of persons-as-role-holders or office-bearers and the like, and of social practices involving both expressive and practical aims and outcomes.” From such evidence, the consensus seems to be that an institution is a set of norms, rules of behaviour, etc. that creates a structure of interacting roles into which participants in the institution fit, and which is seen to have the function of achieving some end (whether or not it also has other functions.)

The interactions defined by the norm formation have effects on the individual agents in the ensemble but they are defined in terms of subsets of the ensemble. The norm formation that is constitutive of the ensemble describes its functions and the means by which they are to be performed. Moreover, the rationality of any such norm formation will be judged by the consistency of its propositions with the supposed functions to be performed. However, the fact that there is a supposed ‘function’ for an institution is not essential to its sociological characterization. That essential character is rather the system of interactions and roles that are created by the norm formation that characterizes the ensemble. In what follows therefore, institutions will be defined in terms of their sociologically relevant characteristics in the first place, and may then be tested for satisfactoriness in the theories in which institutional entities have a place. So:

Let X be a set of agents, R = {r₁, …, r_n} Ì 2^X with (“x Î X) ($r_i Î R) [x Î r_i], N a norm formation.

Î = (X, R, N) is an Institution if

1. N Ì N_O(X)
2. (“r_i Î R) ($n Î N) ($r_j Î R) (“x Î r_i) ($C_x Ì k_x) (“c_x Î C_x)

[g(n, c_x) & ($y Î r_j) ($a_x Î a_x) [g(n, a_x) & e(x, a_x, c_(x,y}, q_y, y))] ]

• R(Î) = R is the Roleset of Î. The elements of R(Î) are the Roles of Î
• |Î| = X is the membership of Î
• N(Î) = N is the Ruleset of Î. The elements of N(Î) are the Rules of Î

Let Î = (X, R, N) be an institution, r_i, r_j Î R. Write ár_i, r_jñ_N iff

($n Î N) (“x Î r_i) ($C_x Ì k_x) (“c_x Î C_x)

[g(n, c_x) & ($y Î r_j) ($a_x Î a_x) [g(n, a_x) & e(x, a_x, c_{x,y} , q_y, y)]]

• e. There is a norm in N such that in contexts governed by that norm, and for any x in r_i there is an action governed by that norm that has an act effect on some y in r_j.
• Read this as r_i Acts On r_j Under N (or r_i Acts On r_j In Î)
• N: r_i ¾® r_j, or, if the action element is part of a graphical representation of a collection of actions all governed by the same norm formation, then let N be a label for that representation.
• Alternatively, Î: r_i ¾® r_j
• Note that this is modelled on the definition given for agent interactions
• IRAD(Î) = {<r_i, r_j>: r_i, r_j Î R(Î), ár_i, r_jñ_N}, the Institutional Role Action Diagram.

Let Î₁ = (X₁, R₁, N₁) and Î₂ = (X₂, R₂, N₂) be institutions.

1. If ($r Î R₁) ($q Î R₂) q Ì r then Î₂ Supports Î₁
2. If ($r Î R₁) ($q Î R₂) q = r then Î₁ and Î₂ Intersect

 

Examples:   A typical institution is the Family. Now the family, like many other institutions – and all the most interesting ones – has a vast number of constitutive norms, most of them informal or unexpressed, and which differ from instance to instance of the institution. The family in Saudi Arabia or China is a different institution from the family in Australia. It’s certainly also true that different versions of the institution are to be found within what generally count as social boundaries: for example, the family of Black-Americans is different from the family of Ozark Americans. The subdivisions of normative typology can be made presumably down to an arbitrarily low level if we assume that the only reasonable way to operationalise the concept of belief or desire is to infer it from the behaviours that they are supposed to produce in an intentional agent. (The nature of the constitutive norms is a vital topic of sociological study.) To speak of a family in loose terms, however, is to speak necessarily of an idealised or common or otherwise generalised version. We shall consider only a fragment of a standardised version of the institution of the family here.   Let Family be Îfamily = (X, Rfamily, Nfamily) X is the general population of the society in question.             Nfamily = {n1, n2, n3, n4, …} where n1 = ‘If a man and woman have a child then they should be the father and mother of that child’ n2 = ‘Parents don’t have sex with their children’ n3 = ‘Parents protect their children’ n4 = ‘Parents should be married’ … ·         Note that the norm formation proposed for this institution includes explicit definitions for some of the role memberships. That is not necessarily true of all institutions, for which the norm formations may appeal to concepts defined elsewhere.             Rfamily = { r1, r2, r3, r4, …} where r1 = Fathers      = {x: x Î X & Male(x) & ($y Î X)[Offspring_of(y, x)]} r2 = Mothers     = {x: x Î X & Female(x) & ($y Î X)[Offspring_of(y, x)]} r3 = Parents      = {x: x Î r1 Ú x Î r2} r4 = Children    = {x: x Î X & ($y Î X)[ Offspring_of(x, y) ])} r5 = Married Persons … ·         Membership of the role of ‘Married Person’ is not defined by the norms included in the fragment above. ·         The predicate functions used above are undefined, but have the obvious definitions.   It is clear even from the fragment presented that institutions do not exist in isolation. It may turn out that each institution essentially depends for its character upon its position in a system of interlocking institutions – in the same way that the meanings of words in a language can hardly be said to exist in isolation. To illustrate the systematic nature of institutions we present a fragment of a formal model of the institution of Marriage.       Let Marriage be Îmarriage = (X, Rmarriage, Nmarriage) X is the general population of the society in question.             Nmarriage = {n1, n2, n3, n4, …} where n1 = ‘parents should be married’ n2 = ‘A man and a woman who are married have sex only with each other’ n3 = ‘A married couple cooperate’ n4 = ‘A marriage is performed by a celebrant’ …             Rmarriage = { r1, r2, r3, r4, …} where r1 = Males r2 = Females r3 = Celebrants = {x: x Î X & ($y,z Î X)[ Marries(x, y, z) ])} r4 = Married Persons    = {x: ($y,z Î X)[ Marries(y, x, z) ]} r5 = Parents … ·         Here membership of the role of ‘Married Person’, which was not defined in the institutional norms of marriage above, is defined by the institutional norms of marriage. ·         r5 Î Rfamily = r4 Î Rmarriage (amongst others) so Îfamily intersects with Îmarriage and these two institutions support one another. ·         Note that the role of married persons might very well be defined by the appropriate norm formations as {x: ($y,z Î X)[ (Male(x) Û Female(z)) & Marries(y, x, z) ]} which indicates how the recent controversy over ‘same-sex marriage’ may be interpreted as a controversy not just over moral rights but over the very constitution of the institution of marriage. ·         Note that in the two examples given, the participants in the institutions are assumed to be the general population. That is simply a convenience and is probably not accurate.

Institutional Functions

Questions must arise as to the degree to which any set of norms can be unambiguously identified as forming a natural basis for an institution. Two observations may be made with respect to this: first, that the identification of such norm formations is an appropriate study of sociologists and will be sensitive to the type of theory being proposed (as it is unlikely that institutions form natural kinds;) and second, that the most profitable direction of enquiry into the ‘essence’ of any institution must be toward the function of the institution.

Ideal Functions

Let X be a set of agents in the general population of the society in question.

Let Î = (X, R, N) be an institution as defined.

We define an Ideal Institutional Context Consequence Function as:

            C_I(Î, c_X,0, X) = c_X,1 iff

(“x Î X)[ g(N, c_x,0) Þ [(a_x,0 = A_x(q_x,0, c_x,0)) Þ (£_N(a_x,0)Ú¯_N(a_x,0)]] Þ C(a_X,0, c_X,0, X) = c_X,1

• In the above we make the obvious extension to the context consequence function:

C(a_X,0, c_X,0, X) = È_xÎX C(a_x,0, c_X,0, X).

• In most reasonable interpretations of the modal operators modal disjunction above could be replaced with a simple ¯
• Although the IICCF uses the same function letter as the standard context consequence function, the functions are easily distinguished by the arguments.
• The function is an ideal function since the definition describes the context consequence of every relevant agent doing as the institutional norms require. This is never likely to be the actual situation even if every agent was an acceptant of those norms – unless the norms simply describe the actions of every agent, in which case it will apply by fiat; but we discounted that interpretation of norms in the relevant chapter.

What we mean by the function of an institution may not, however, be best captured by defining it as the immediate consequence of the relevant agents acting consistently with its norms. It may be that given certain sorts of contexts as starting points, the immediate consequence of the operation of the institution does not achieve the intuitively felt ‘function’ of that institution. Thus we may seek a definition that captures the notion of ‘in the long run’.

We describe the Ideal Institutional Context Consequence Sequence as:

C_I(Î, c_X,0, X) = <c_X,i: 0 < i, c_X,i+1 = C_I(Î, c_X,i, X)>

One possible notion of function might be:

            c is an ideal function of Î iff ($i)[c Î C_I(Î, c_X,0, X)_i]

This would, however, have the consequence of making trivialities or human universals be the functions of any institution. For example, the fact that humans walk on two legs would on this definition be a consequence of the institution of Marriage, since it occurs in every context of the ideal institutional sequence. This is unlikely to be a satisfactory notion.

Define instead an Ideal Strict Institutional Context Consequence Function as:

            C_I^S(Î, c_X,0, X) = c_X,1 iff c_X,1 = { p Î C_I(Î, c_X,0, X):

1. (“x Î X)[ g(N, c_x,0) Þ [(a_x,0 = A_x(q_x,0, c_x,0)) Þ (£_N(a_x,0)Ú¯_N(a_x,0)]] Þ

p Î C(a_X,0, c_X,0, X) &

1. ($X’ Ì X)(“x Î X’)[ g(N, c_x,0) & (a_x,0 = A_x(q_x,0, c_x,0)) & ~(£_N(a_x,0)Ú¯_N(a_x,0)] Þ

p Ï C(a_X,0, c_X,0, X)       }

• p is a propositional description of some fact concerning the context of x or X as appropriate. Each context c_x or c_X is a set of such propositions. This was simply assumed to be clear earlier, but now needs to be made explicit.

And the Ideal Strict Institutional Context Consequence Sequence as:

C_I^S(Î, c_X,0, X) = <c_X,i: 0 < i, c_X,i+1 = C_I^S(Î, c_X,i, X)>

In fact according to the normal usage of the term ‘function,’ we have already defined an ideal institutional function in the definition of the ideal strict institutional context consequence function; however, the use of the term in the discussion of institutional functions generally is best understood as a predicate or predicates, which we may define thus:

            p or c is an Ideal Institutional Function of Î given c_X,0 iff        ($i)[c Î C_I^S(Î, c_X,0, X)_i] or

($i)[c Î C_I^S(Î, c_X,0, X)_i & p Î c]

• p a proposition, c a context as used above
• where c_X,0 is understood we may disregard it
• write F_I(Î)(c_X,0)(p) or F_I(Î)(c_X,0)(c)
• an ideal institutional function p is Transient if
  (“i)[(c Î C_I^S(Î, c_X,0, X)_I & p Î c) Þ ($j>i)(“c)[c Î C_I^S(Î, c_X,0, X)_j Þ p Ï c] ]

and similarly for the ideal institutional function c.

• an ideal institutional function p is Recurrent if
  (“i)[(c Î C_I^S(Î, c_X,0, X)_I & p Î c) Þ ($j>i)(“c)[c Î C_I^S(Î, c_X,0, X)_j Þ p Ï c] ] &

(“i)(“c)[(c Î C_I^S(Î, c_X,0, X)_i Þ p Ï c) Þ ($j>i) [c Î C_I^S(Î, c_X,0, X)_j & p Î c]]

and similarly for the ideal institutional function c.

Note that every recurrent institutional function is transient.

• an ideal institutional function p is Enduring if
  ($j)(“i>j)($c)[c Î C_I^S(Î, c_X,0, X)_i & p Î c]

and similarly for the ideal institutional function c.

Real Functions

Most of the hard definitional work has now been done and we can proceed more quickly through definitions of more immediately useful institutional characteristics. The ideal function of an institution is of interest for someone who wishes to design an institution or who wishes to understand the intention of one who plans an institution, but it is unlikely to accurately describe the function of the institution as it actually operates. That function depends upon being an acceptant – or behaving as an acceptant – of the norms that constitute the institution, but we accepted that for various reasons these norms might not always be followed even by an ‘acceptant.’ It was proposed, for example, that we could adequately capture the belief that x will not contravene n unless he estimates that the total satisfaction to be gained from doing so is sufficiently greater than the satisfaction to be gained from abiding by n in the condition:

B_x[ n ] Þ ($C_x,applies Ì k_x) ($a_x,bad Ì a_x) (“c_x,applies Î C_x,applies) (“a_x Î a_x,bad) (“c_x,0 Î k_x)

[((c_x,0 = c_x,applies Þ n & a_x |– ^) &

~B_x­[ (“a_x,alt ¹ a_x)[T(C(a_x,alt, c_x,0, x), I_x, x) << T(C(a_x, c_x,0, x), I_x, x)] ])

Þ A_x(q_x,0, c_x,0) ¹ a_x]

Should this be the case, or should some other interference in the ‘ideal’ action of the acceptant of the institutional N occur, the ideal function may fail. We need therefore to speak of the actual institutional functions.

Let X be a set of agents in the general population of the society in question.

Let Î = (X, R, N) be an institution as defined.

We define an Institutional Context Consequence Function as:

            C(Î, c_X,0, X) = c_X,1 iff (“x Î X)[ x Î K(N) & a_x,0 = A_x(q_x,0, c_x,0)] Þ C(a_X,0, c_X,0, X) = c_X,1

• The institutional context consequence function describes (obviously) the real consequence of the institution.
• In the above we must take into full account the brief considerations made when introducing norm-directed behaviour that the action function will need to account for ‘degrees of belief’ in the norms, possible irrationality, possible epistemological limitations, etc.

We describe the Institutional Context Consequence Sequence as:

C(Î, c_X,0, X) = <c_X,i: 0 < i, c_X,i+1 = C(Î, c_X,i, X)>

Define a Strict Institutional Context Consequence Function as:

            C^S(Î, c_X,0, X) = c_X,1 iff c_X,1 = { p Î C(Î, c_X,0, X):

1. (“x Î X) [ x Î K(N) & a_x,0 = A_x(q_x,0, c_x,0)] Þ p Î C(a_X,0, c_X,0, X) &
2. ($X’ Ì X)(“x Î X’) [ x Ï K(N) & a_x,0 = A_x(q_x,0, c_x,0)] Þ p Ï C(a_X,0, c_X,0, X) }

And the Strict Institutional Context Consequence Sequence as:

C^S(Î, c_X,0, X) = <c_X,i: 0 < i, c_X,i+1 = C^S(Î, c_X,i, X)>

Which leads us to the definitions of appropriate predicates as:

            p or c is an Institutional Function of Î given c_X,0 iff     ($i)[c Î C^S(Î, c_X,0, X)_i] or

($i)[c Î C^S(Î, c_X,0, X)_i & p Î c]

• write F(Î)(c_X,0)(p) or F(Î)(c_X,0)(c)
• The obvious modifications give us also transient, recurrent, and enduring institutional functions.

Intentional Functions

When (“x Î X)[D_x[F(Î)(c_X,0)(p) ]] we may speak of p being the Desired Institutional Function, F_D(Î)(c_X,0)(p)

If (“x Î X)[B_x[F(Î)(c_X,0)(p) ]] the p is the Believed Institutional Function, F_B(Î)(c_X,0)(p)

The concepts of manifest and latent function were introduced into sociology by Robert K. Merton (1957, Social Theory and Social Structure, New York: Free Press of Glencoe, p. 51). He states there that manifest functions are “those objective consequences contributing to the adjustment or adaptation of the system which are intended and recognised by participants in the system,” while latent functions are simply “those which are neither anticipated nor recognised.” They can be defined using the tools developed above. Thus:

If F(Î)(c_X,0)(p) & (“x Î X)[D_x[F(Î)(c_X,0)(p) & B_x[F(Î)(c_X,0)(p)]] then p is a Manifest Institutional Function, F_M(Î)(c_X,0)(p)

If F(Î)(c_X,0)(p) & (“x Î X)[ ~D_x[F(Î)(c_X,0)(p) & ~B_x[F(Î)(c_X,0)(p) ]] then p is a Latent Institutional Function, F_L(Î)(c_X,0)(p)

• Whether this is exactly what Merton had in mind however is open to dispute (Helm, P. 1971, ‘Manifest and Latent Functions’ The Philosophical Quarterly, v. 21, no. 82, pp 51-60) since X (the relevant set of agents) is not defined, it isn’t known whether the universal quantifier is intended here, it’s not clear what is intended by ‘unintended,’ etc.
• Nor are there distinctions made between transient, recurrent, or enduring functions.
• Merton also desired to distinguish between functions and ‘dysfunctions’, which do not assist the system to adapt and adjust to the environment – but there is no such distinction made above.
• In short, it isn’t obvious that this is a necessary or useful pair of institutional functions

If F(Î)(c_X,0)(p) & (“x Î X)[~D_x[F(Î)(c_X,0)(p)] then p is what Merton would call an ‘unintended consequence,’ and in the current terminology we might label it the Undesired Real Institutional Function.

Institutional Norms

From the above it seems that it is possible to use the notion of action governed by norms to define a ‘function’ of an institution. It is also possible to use the notion of the function of an institution to determine the ‘essential’ norms of an institution. The point of this is to attempt to establish the boundaries of an institution. For example, referring to the examples above, does the institution of Marriage as understood by the relevant agents exclude, normatively, homosexual pairings? Does the institution of Family allow polyamorous unions or divorces?

Let p be such that F(Î)(c_X,0)(p) for Î = (X, R, N).

Suppose that

1. ($N₁ Ì N) F(Î₁)(c_X,0)(p) for Î₁ = (X, R₁, N₁) and
2. (“N₂ Ì N₁)~F(Î₂)(c_X,0)(p) for Î₂ = (X, R₂, N₂)

We may say that N₁ is a Minimal Norm Formation for the function p of the institution Î

• There is no reason to think that any minimal norm formation is unique.
• Note that the functions of an institution are not assumed to be unique, and the set of minimal norm formations for p in Î will also vary with that variable.

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