Agency contrasts sharply with a grant of property rights. The grantee, the person to whom property is granted, is bound by the rules of the grant, not by the will of the grantor. A grantor can cause his interests to be represented only through specifying, before the grant is made, the conditional rules under which the grant is made. Within the grant condition and boundary rules, the owner of property is legally expected to act solely in his own interests. With political property rights, the “boundaries” are rules of legal procedure which the owner may not breach. A similar but temporary effect can sometimes be achieved with a contract that details all of the rules of the relationship, with the legal and moral understanding that all else about the relationship is simply a matter of personal preference rather than of one party learning and implementing the preferences of the other.
Representation distance estimates the degree of loss of information, control, or both in a principal/agent relationship. In other words, it estimates the degree to which the agent fails to know or implement the true preferences of the principal(s). In a representative democracy or republic, representation distance estimates the degree to which the representative actually represents the interests (basically equivalent to economic preferences, but in politics they might also include preferences to coerce others) of his constituents rather than others.
Representation distance generally grows with the size of group represented. Since even any two people communicate imperfectly, and have conflicts of interest between them, it's not even possible for one person to perfectly represent another, albeit such representation can far more accurately represent any interests than representing a group. One can think of this distance as being minimal, call it 1, when a person is acting for himself. When one principal delegates duties to one carefully chosen and monitored agent (a.k.a. representative), the distance is some greater value, perhaps 2. Representation distance is further compromised by majority vote, which leads to two losses: (1) the interests become increasingly general and vague, rather than the specific and concrete interests the voters actually have, as the number of voters increase and (2) the interests of minorities tend to be neglected. These numbers are purely illustrative (perhaps we should start at zero), and the function whereby representation distance increases with the size of the group represented is unknown.
A similar effect occurs in shareholder/management relationships. Shareholder interests vary greatly. Their time preferences for dividends or capital gains vary greatly. They sometimes have non-monetary interests, as in "socially conscious" investing. But the duty of management to shareholders usually gets stripped down to a very simple one, a fiduciary duty to maximize profit.
There may also be efficiency measures proportional to representation distance. For example, the efficiency of investment in public goods (where the "public" is just the population of voters) may be some function of the number of voters. On the other hand, larger representation distance may have a good effect in decreasing the ability of some voters to coerce or oppress other voters via the representative.
Vast amounts of money are put into K Street lobbying, primarily by corporations and government employee labor unions. This is readily explained by representation distance: the relationships between lobbyists and Congressmen, and even more between lobbyists and unelected but influential bureaucrats, often have a much shorter representation distance than those between voter and Representative. (The much shorter physical distance, which greatly facilitates face-to-face relationships, greatly helps to shorten the representation distance, but these are otherwise independent ideas). We can thus expect persons with sufficient resources at stake, such as corporations and government employee unions, to put far more effort into lobbying than they or others do into mere voting.
Since a political representative represents not the only normal economic preferences of voters, but also preferences to coerce others, large representation distance is not necessarily a bad thing. An effectively infinite representation distance is effective independence, which is often a good thing. (We can’t achieve perfectly infinite representation distance, of course). We want the legislative, executive, and judicial branches to operate independently, for example, not for one to represent the other. However political property rights, or contracts where when the rules are unspecified on party is not expected to learn or implement the preferences of the other, are usually a far better way than pseudo-representation to achieve independence or infinite representation distance. Political property rights turn at least putatively will-based (a representative is supposed to represent the will of his principal(s)) system into a rule-based system (the owner must operate within the procedural bounds of his property right, and is expected within those rules to learn and follow only his own preferences). Pseudo-representation -- the use of the language of agency depsite a very large representation distance -- may, however, provide an illusion of participation sufficient to satisfy the naive that their interests are actually being represented.
To summarize, no group is truly homogenous, so it's not possible to perfectly represent any group. Since even any two people communicate imperfectly, and have conflicts of interest between them, it's not even possible for one person to perfectly represent another, albeit such representation can far more accurately represent any interests than representing a group. Thus representation distance grows with the size of group represented. Much politics can be explained by problems caused by representation distances that are too long or too short, or by poor estimates of representation distance made by naive participants.
[These comments are based on my comments on a previous post, and thanks to "anonymous" for reminding me about my old idea of representation distance, and for the idea that bribery of a representative by a third party increases representation distance from the principal].
Here are some links to learn about agency law, the principal/agent problem, and political property rights.