Notes on The Concept of Power by Robert A. Dahl

Power as a Relation Among People

• Power is defined as a relation among actors (people or groups) in which one actor (A) can get another actor (B) to do something B would not otherwise do.
• Actors can be individuals, groups, roles, offices, governments, or nation-states.
• A complete statement of power should specify: (a) base of power, (b) means/instruments, (c) amount/extent, (d) scope of responses.
• The base of power comprises all resources that can be exploited to affect behavior (e.g., patronage, veto, access to audiences, charisma).
• The means are the mediating activities that exploit the base (e.g., promising, threatening, appealing, conferences).
• The scope is the range of B’s possible responses that can be influenced.
• Power is modeled probabilistically: the amount of power can be represented by a probability statement about how likely B is to respond in a given way after A acts.
• Basic notation (2×2 case) for clarity:
  • (-4, w) = A performs action w; (a, x) = B (the respondent) performs response x.
  • P( a, x | A, w ) = probability that B does x given A does w.
  • P( a, x | A, ¬w ) = probability that B does x given A does not do w.
  • The power measure is M = P(a, x \,|\, A, w) - P(a, x \,|\, A, \neg w)

Formal Definition and Properties of Power

• A necessary condition for a power relation: there must be a time lag between A’s action and B’s response (some connection may be required).
• There is no action at a distance; there must be a connection or opportunity for a connection between A and B.
• A third condition: power involves a successful attempt by A to get B to do something B would not otherwise do. However, power should not be equated with causality; power is a relation, not simply a cause.
• Independence condition: if P(a, x | A, w) = P(a, x | A, ¬w), then M = 0 (no power; statistical independence).
• Max/min of M:
  • M is maximized when P(a, x | A, w) = 1 and P(a, x | A, ¬w) = 0.
  • M is minimized when P(a, x | A, w) = 0 and P(a, x | A, ¬w) = 1.
• Negative power is possible: a negative M indicates that A’s action reduces the likelihood of the response compared to not acting. Negative power is conceptually allowed and can occur in some cases (e.g., a commanding action that leads to a counterproductive outcome).
• The direction of power (which way the effect goes) depends on how one defines the response and the direction of the outcome; it need not reflect the actor’s intent.
• In Dahl’s framework, the same basic idea can be applied to different contexts (e.g., political actors) and can be operationalized in multiple ways depending on data availability and research goals.

Power Comparability and Ranking

• Power comparability requires that the actor, base, means, respondents, and responses/scopes be comparable across actors.
• There is no single universal scale for power; comparability is an undefined notion that must be interpreted in light of research goals and available data.
• When comparability holds, actors can be ranked by the amount of power they possess (transitivity generally holds in principle): if M(A) > M(B) then A is more powerful than B for the given set of respondents and scope.
• In practice, one must define:
  • The set of respondents (e.g., Senators, voters, officials).
  • The set of responses (e.g., votes, decisions, actions).
  • The scope of responses (e.g., which outcomes count).
  • The direction of the outcome (what counts as “for” vs “against”).
• Because real data are limited, researchers often need to make pragmatic choices about comparability, which can influence rankings significantly.

Measures for Comparing Power in Practice

• Measure M* (aggregate effect across a controller’s behavior):
  • For a given actor A and respondent set, define for a given issue the probabilities when A acts to favor and when A acts to oppose; and when A does nothing.
  • Let pfor = P(outcome | A favors the measure), pagainst = P(outcome | A opposes the measure).
  • Define M* = pfor − pagainst (a maximum of 1, minimum of −1; 0 means no net effect).
  • M* can be shown to reduce to a simpler form in some settings: M^* = p(a\,|\, x, A, w) - p(a\,|\, x, A, \neg w).
• Practical note: M* depends on comparing against a baseline of doing nothing; it relies on data about behavior when A acts, and when A does not act.
• M" (pairwise comparison measure):
  • An alternative to M* that uses paired comparisons between two actors (e.g., two Senators).
  • For a pair (Si, Sj): estimate the change in the probability of a legislative outcome when Si favors the bill vs when Si opposes it, holding Sj’s position fixed, and compare similarly for Sj.
  • In practice, use absolute differences to avoid sign ambiguity: |Mi| vs |Mj|, and compare across pairs accordingly.
  • This method emphasizes relative influence within pairs and can be sensitive to which bills are considered and how differences are measured.
• The choice between M* and M" (and other operational measures) yields different rankings, illustrating the sensitivity of power comparisons to data and definitions.

Practical Issues and the Senate Applications

• Dahl, March, and Nasatir applied these ideas to rank 34 U.S. Senators for foreign policy and tax/economic policy influence (1946–1954).
• Data limitations:
  • Roll-call votes are used as proxies for prior positions; this creates the “chameleon” problem where a Senator who just cases votes according to the majority can appear influential even if he has little independent influence.
  • The “chameleon” problem (and the satellite problem) shows that rankings can be artifacts of data and method, not true influence.
• The “chameleon” issue: a Senator who follows another leader’s lead on all issues could rank highly under certain measures without actual independent influence over outcomes.
• The “satellite” issue: an actor who always follows a leader’s line could have high apparent influence in certain pairwise comparisons but little autonomy.
• A key practical lesson: comparability and the definition of the set of issues (what counts as a comparable response) matter greatly for the interpretation of ranks.

Data, Comparability, and Research Strategy

• Power comparability is undefined in general and must be defined for each study, based on goals, available data, and theoretical constructs.
• The researcher must decide which issues count as comparable, which respondents are comparable, and which outcomes (responses) are appropriate for ranking.
• A single universal ranking is unlikely; researchers should aim for context-dependent rankings that are theoretically meaningful and methodologically transparent.

Operational vs Conceptual Perspectives: A Dialogue

• C (Conceptual): The power of A over a with respect to x is measured by M = P(a, x \,|\, A, w) - P(a, x \,|\, A, \neg w). This allows ranking of actors given comparable contexts.
• O (Operationalist): In practice, data are limited, and power is not a single monolithic concept; different operational definitions yield different results. We may need multiple, context-specific power concepts (Power 1, Power 2, etc.).
• C: Even with data limits, the formal concept provides a standard for evaluating and improving operational measures; it helps identify where measures are defective and guides the development of better methods.
• O: While the data may be imperfect, abandoning the concept altogether would discard a valuable framework for understanding and comparison. The formal notion serves as a reference point for evaluating operational approaches.

Conclusions and Implications

• The concept of power as a relation among actors provides a rigorous framework for thinking about influence, but its practical application requires carefully defined comparability and suitable data.
• There is no single, universal theory of power; researchers should adopt problem-specific definitions and be explicit about comparability criteria.
• Operational measures (like M* and M") are useful, but their limitations must be acknowledged; they should be interpreted as approximations to the formal concept.
• Studying power can reveal the strengths and gaps of available data and motivate the development of better observational and measurement techniques for social influence.

References (Selected)

• 1. Dahl, R. A., March, J., & Nasatir, D. Influence ranking in the United States Senate. Read at APSA annual meeting (1956).
• 2. French, J. R. P. Jr. A formal theory of social power. Psychol. Rev. (1956).
• 3. Lasswell, H. D., & Kaplan, A. Power and Society. Yale Univ. Press (1950).
• 4–11. March, J. G.; Luce, R. D.; Shapley & Shubik; Simon; Weber; etc. (See article for full references).