Relationships:

In any relationship (R), there are two individuals (P¹ and P² ). The possible types of relationships are relatively infinite (R^∞ ), and may include unexpected relationships like grass clippings in exchange for sex ("fetish?"). For any specific relationship (R^n), there will be associated costs (Cⁿ ) and benefits (Bⁿ⁾ and benefits to each individual engaging in that relationship.

• P1 (Bⁿ - Cⁿ ) ◄Rⁿ ► P2 (Bⁿ - Cⁿ )

Costs and benefits of a relationship can be said to be the subjective positive ( ) and negative (-) value (V) of a relationship.

• Cost: C = V^-
• Benefits: B = V
• Total Value: Bⁿ - Cⁿ = V - V^- = V^Δ

Value is specific to the individual changes from one person to the next, often in highly unexpected ways due to unknown and unexpected reasons. While similarities may exist, the costs and benefits between any random individuals (P^x and P^y ) are rarely identical.

• P1(V^Δ ) != P2(V^Δ )
  

Swapping individuals in the relationship quickly results in disaster:

• An intelligent entrepreneur (P¹ ) may hire for $100 per hour (Rⁿ ) an electrical engineer (P² ) to help develop a processor for a new advanced smart phone, and as a result reap major profits.
• A creative artist (P³ ) attempting to hire for $100 per hour (Rⁿ ) an aroma therapy expert (P⁴ ) to help develop microprocessors would likely result in a massive failure.

Opportunity Cost

Consider the alternative chosen in the absence of an available opportunity (such as Rⁿ ) to be our standard of measurement (V⁰ ). This is known as "opportunity cost,"

• Opportunity Cost is the cost (not restricted to monetary or financial costs) of any activity measured in terms of the value of the best alternative that is foregone. It is the sacrifice related to the second best choice among several mutually exclusive alternatives.

Opportunity cost (V⁰ ) could be considered the natural or default state in the absence of opportunity (i.e. Vⁿ relative to V⁰ ).

Desire, Action, and Inaction

An individual's desire to engage in a relationship could be determined as a subjective perception of the value (V^Δ ) of the relationship, relative to alternatives (V⁰ ).

Consider an individual's desire (D ^/- ) to engage in a relationship, as relative to their desire for the opportunity cost (D⁰ ). If an individual determines the value of a relationship to be better than the opportunity cost, a person can be said to desire the relationship. Conversely the perceived value is less than the opportunity cost, then it can be said a person does not desire the relationship.

• if (Vⁿ > V⁰ ) then (D )
• if (Vⁿ < V⁰ ) then (D^- )

Consider the desire for a specific relationship between two individuals

• P1 (D^- ) ◄Rⁿ ► P2(D^- ) ... Neither desires relationship
• P1 (D ) ◄Rⁿ ► P2(D^- ) ... Person 1 desires relationship, Person 2 does not desire relationship
• P1 (D^- ) ◄Rⁿ ► P2(D ) ... Person 1 does not desire relationship, person 2 desires relationship

• P1 (D ) ◄Rⁿ ► P2(D ) ... Both desire relationship

• Given both desire to participate in a relationship (D )and the relationship occurs, both perceive an increase in value of their opportunity cost and the relationship will likely occur naturally, consistent with desires of both parties.

• Given both desire to not participate in a relationship (D^- )and the relationship does not occur, both perceive the opportunity cost to be superior, and inaction towards a relationship is consistent with desires of both parties.

• Given both desire to not participate in a relationship (D^- ), and the relationship will likely not occur naturally, leading to each pursuing their opportunity costs (Alt ), and the inaction towards the non-relationship is consistent with the desires of both parties.

• Given one party desires a specific relationship and another does not (P1 (D ) ◄Rⁿ ► P2(D^- )), a conflict of desires (i.e. conflict of interest) occurs. Action towards this relationship will be against the desires and subjective valuation relative to opportunity cost of one individual. Due to the near infinite possible types of relationships (R^∞ ) amongst 7-billion people (P^3....7Bill ), no individual could be said to be more obligated to act on a specific arbitrary relationship that they do not desire, than any of the infinite other relationships not engaged in every day. Further, attempts to apply this universally quickly break down into a contradictory and illogical mess (i.e. I decree I can murder you and you can't murder me, you decree the reverse).

Third Party:

If a third party (P³ ) interferes in a relationship between two individuals, the two individuals are now said to have an (involuntary?) relationship with the third party. This point is important to avoid conflation of unrelated interactions, relationships, and desires.

Imposing and Coerced Relationships

Given an individual's (P¹ ) desire to not participate in a relationship (R), the most common methods for another to cause this relationship a reality are....

• Positive Incentives: Defined: actively altering the conditions of a relationship so that the relationship becomes desirable ( D ) to the other party.
• Imposing Defined: actively forcing a relationship (R) on an individual regardless of the desires or actions of the other individual. Forcing, referring to overpowering the other individual's actions and desires.
• Coercion: Defined: actively imposing undesirable conditions or perceptions on available alternatives (opportunity cost, R2), as to make the relationship (R) relatively desirable than the new imposed opportunity cost (R2).
• Fraud: Defined: Actively misinforming another individual as to influence an individual into a relationship (R), whereby that individual would not have participated otherwise.

P.S. From here my intent is to connect imposing, coercion, and fraud (non-consensual relationships) to desires, their value, and the ultimate destructive and parasitic nature. Further this leads towards implications on what cannot be said to be coercive (against the desires) on the basis of a weak or general argument (i.e. "do employment relationships automatically imply coercion?"). Feedback, analysis, suggestions, and critiques wanted.