The Exit, Voice, Loyalty (EVL) model or Exit, Voice, Loyalty, Neglect (EVLN) is used in the fields of comparative politics and organizational behavior. It is an extensive form game used to model interactions typically involving negative changes to one player's environment by another player. These concepts first appeared in Albert Hirschman's more broadly focused 1970 book, Exit, Voice, and Loyalty: Responses to Decline in Firms, Organizations, and States. A common use in political science is between citizens and their government. Usually in this use the Citizen player is any group within a society ranging from a single individual to the citizenry as a whole.
Model
The EVL Model involves two agents and their responses to a change initiated before the game began. The first agent is commonly referred to as the Citizen and the second is commonly referred to as the Government. EVL assumes that the change implemented before the game began was performed by the Government and negatively harms the Citizen.
Formal Definition
The formal definition of EVL is the following:
There are two players: . The moves first, and chooses among three actions . If the chooses , then can either or . If the chooses to , the then chooses between or . Subsequent to this (and any other action choices), the game terminates.
Formally, this is represented by the set of histories The terminal histories, upon reaching which the game terminates, is given by For all other histories, one of the two players makes a move, and this is given by the player function
The utility function of the is defined as
In words, the incurs a cost of whenever they choose to raise their , and if the , they get a payoff of . Irrespective of this choice, they can choose to for a payoff of or remain for payoff of zero.
Similarly, the payoff function of the is defined as
In words, the incurs a cost of one for to the concerns, and gains a payoff of if the does not .
Theoretical Definition
The precursory policy that the Government has implemented has the effect of removing a benefit with the value of 1 from the Citizen and giving it to the Government. The value was chosen to be 1 so that all comparisons within the game can easily be converted to ratios and then adapted to other situations where the true value of the benefit is known.
In EVL, all possible actions that can be taken by the Citizen are grouped into one of three options. Exit options are those in which the Citizen accepts the loss of the benefit and instead alters their behavior to get the best possible alternative. Examples could include relocating assets to avoid a new tax, reincorporating a business to avoid new regulations, buying goods from a different store when the quality of the original diminishes, voting out the incumbent, etc. The payoff of an Exit option for the Citizen is the variable E and the Government gets to keep the 1 it took initially.
Loyalty options are ones where the Citizen chooses to put up with the new policy and not alter their behavior. The payoff for the Citizen is 0 as they decide to take the loss and the Government receives the 1 it took plus the value of the Citizen's Loyalty. The value of the Citizen's Loyalty is the variable L.
Voice options are where the Citizen makes an active effort to show their dissatisfaction with the new policy and tries to get the Government to change its mind. Examples could be lobbying, protesting, petitioning, etc. Voice options do not have immediate payoffs but are intended to give the Government a chance to Respond to the Citizen and revert the policy. In the event the Government does Respond, the payoff for the Citizen is the 1 the Government initially took minus the cost of using Voice. This cost is the variable c. If the Government chooses to Ignore then the Citizen can still Exit or remain Loyal. No matter what the Citizen chooses, they still have to bear the cost of using their Voice and so the payoff for Exit would be E - c and 0 - c for remaining Loyal. The Government would receive the payoff of L (the value of the Citizen's Loyalty) if they chose to Respond and revert the policy, 1 if they chose to Ignore and the Citizen Exits, and 1 + L if they Ignore and the Citizen chooses to remain Loyal.