The correct answer is option 3: Political will of the ruler. This option is not a source of political legitimacy. Let`s examine the other options to gain a better understanding:

Option 1: Consent - Consent refers to the agreement or approval of the people towards a governing authority. When individuals willingly agree to be governed by a particular authority, the legitimacy of that authority is derived from their consent. Consent can be expressed through democratic elections or other forms of public participation.

Option 2: Rational prudence - Rational prudence refers to the idea that political legitimacy is founded on the rational understanding and decision-making of individuals. Legitimacy can be attained when individuals assess and evaluate the actions and policies of the government based on their own rational judgment.

Option 4: Public reason - Public reason refers to the collective reasoning and justification provided by the government to its citizens. When the government provides transparent and reasoned explanations for its decisions and policies, this can contribute to its legitimacy.

In summary, while consent, rational prudence, and public reason can all be sources of political legitimacy, the political will of the ruler is not considered a source of legitimacy.