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❖♣t✐♠❛• ■♥❢♦r♠❛t✐♦♥ ❈❡♥s♦rs❤✐♣ * ❇♦r✐s •✐♥③❜✉r❣ † ✾t❤ ▼❛② ✷✵✶✾ ❆❜str❛❝t ❚❤✐s ♣❛♣❡r ❛♥❛•②s❡s ❇❛②❡s✐❛♥ ♣❡rs✉❛s✐♦♥ ♦❢ ❛ ♣r✐✈❛t❡•② ✐♥❢♦r♠❡❞ r❡❝❡✐✈❡r ✐♥ ❛ •✐♥❡❛r ❢r❛♠❡✇♦r❦✳ ❚❤❡ s❡♥❞❡r ✐s r❡str✐❝t❡❞ t♦ ❝❡♥s♦rs❤✐♣✱ t❤❛t ✐s✱ t♦ str❛t❡❣✐❡s ✐♥ ✇❤✐❝❤ ❡❛❝❤ st❛t❡ ✐s ❡✐t❤❡r ♣❡r❢❡❝t•② r❡✈❡❛•❡❞ ♦r ❤✐❞❞❡♥✳ ■ ❞❡✈❡•♦♣ ❛ ♥❡✇ ❛♣♣r♦❛❝❤ t♦ ✜♥❞✐♥❣ ♦♣t✐♠❛• ❝❡♥s♦rs❤✐♣ str❛t❡❣✐❡s ❜❛s❡❞ ♦♥ ❞✐r❡❝t ♦♣t✐♠✐s❛t✐♦♥✳ ■ ❛•s♦ s❤♦✇ ❤♦✇ t❤✐s ❛♣♣r♦❛❝❤ ❝❛♥ ❜❡ ✉s❡❞ t♦ r❡str✐❝t t❤❡ s❡t ♦❢ ♦♣t✐♠❛• ❝❡♥s♦rs❤✐♣ s❝❤❡♠❡s✱ ❛♥❞ t♦ ❛♥❛•②s❡ ♦♣t✐♠❛• ❝❡♥s♦rs❤✐♣ ✉♥❞❡r ❝❡rt❛✐♥ ❝•❛ss❡s ♦❢ ❞✐str✐❜✉t✐♦♥s ♦❢ t❤❡ r❡❝❡✐✈❡r✬s t②♣❡✳ ❑❡②✇♦r❞s✿ ❇❛②❡s✐❛♥ ♣❡rs✉❛s✐♦♥❀ ❝❡♥s♦rs❤✐♣ ❏❊▲ ❝♦❞❡s✿ ❉✽✷✱ ❉✽✸ ✶ ■♥tr♦❞✉❝t✐♦♥ ❚❤✐s ♣❛♣❡r ❛♥❛•②s❡s ❛ ❇❛②❡s✐❛♥ ♣❡rs✉❛s✐♦♥ ❣❛♠❡ ❜❡t✇❡❡♥ ❛ s❡♥❞❡r ❛♥❞ ❛ ♣r✐✈❛t❡•② ✐♥❢♦r♠❡❞ r❡❝❡✐✈❡r✳ ❇♦t❤ t❤❡ s❡♥❞❡r ❛♥❞ t❤❡ r❡❝❡✐✈❡r ❤❛✈❡ •✐♥❡❛r ✉t✐•✐t② ❢✉♥❝t✐♦♥s✳ ❚❤❡r❡ ✐s ❛ ❝♦♥t✐♥✉✉♠ ♦❢ st❛t❡s✳ ❚❤❡ s❡♥❞❡r ✇❛♥ts t❤❡ * ■ ❛♠ ❣r❛t❡❢✉• t♦ ❱✳ ❇❤❛s❦❛r ❢♦r ❣✉✐❞❛♥❝❡ ❛♥❞ ❛❞✈✐❝❡✳ ■ ❛•s♦ t❤❛♥❦ t❤❡ ❡❞✐t♦r✱ t❤r❡❡t❤❡ s❡♥❞❡r ✐s r❡str✐❝t❡❞ t♦ ❝❡♥s♦rs❤✐♣ str❛t❡❣✐❡s✿ ❡✈❡r② st❛t❡ ♦❢ t❤❡ ✇♦r•❞ ✐s ❡✐t❤❡r r❡✈❡❛•❡❞ ♣❡r❢❡❝t•②✱ ♦r ♥♦t r❡✈❡❛•❡❞ ❛t ❛••✳ ■♥ ♦t❤❡r ✇♦r❞s✱ t❤❡ s❡♥❞❡r ♣♦♦•s s♦♠❡ st❛t❡s ✐♥t♦ ❛ s✐♥❣•❡ s❡t✱ ❛♥❞ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ♦t❤❡r st❛t❡s s❤❡ s❡♥❞s ❛ ✉♥✐q✉❡ ♠❡ss❛❣❡✳ ❆ r❡str✐❝t✐♦♥ t♦ ❝❡♥s♦rs❤✐♣ str❛t❡❣✐❡s ✐s r❡•❡✈❛♥t t♦ ❛ ♥✉♠❜❡r ♦❢ s✐t✉❛t✐♦♥s ✐♥ ✇❤✐❝❤ t❤❡ s❡♥❞❡r ♥❡❡❞s t♦ ❝❤♦♦s❡ ✇❤❡t❤❡r t♦ tr❛♥s♠✐t ✐♥❢♦r♠❛t✐♦♥ t❤❛t ♦r✐❣✐♥❛t❡s ❢r♦♠ ❛♥ ❡①♦❣❡♥♦✉s s♦✉r❝❡✳ ❈♦♥s✐❞❡r✱ ❢♦r ❡①❛♠♣•❡✱ ❛ ✜r♠ t❤❛t ✇❛♥ts t♦ ♣❡rs✉❛❞❡ ❝✉st♦♠❡rs t♦ ❜✉② ✐ts ♣r♦❞✉❝t✳ ❆ ❝✉st♦♠❡r✬s ✇✐••✐♥❣♥❡ss t♦ ❞♦ s♦ ❞❡♣❡♥❞s ♦♥ ❤✐s ♣r❡❢❡r❡♥❝❡ t②♣❡✱ ❛s ✇❡•• ❛s ♦♥ ❛ st❛t❡ ♦❢ t❤❡ ✇♦r•❞✱ ✇❤✐❝❤ r❡✢❡❝ts t❤❡ ♣r♦❞✉❝t✬s q✉❛•✐t②✳ ❚❤❡ ✜r♠ ❝❛♥♥♦t ❝r❡❞✐❜•② ❝♦♠♠✐t t♦ ❛♥ ❡①♣❡r✐♠❡♥t t❤❛t ♠❛♣s st❛t❡s t♦ ♠❡ss❛❣❡s✳ ■t ❝❛♥✱ ❤♦✇❡✈❡r✱ s✉❜♠✐t ✐ts ♣r♦❞✉❝t ❢♦r r❡✈✐❡✇ ❜② ✐♥❞❡♣❡♥❞❡♥t ❡①♣❡rts✳ ❙♦♠❡ r❡✈✐❡✇❡rs t❡♥❞ t♦ ❞❡t❡❝t ❛♥❞ r❡♣♦rt ✈❡r② ❤✐❣❤ q✉❛•✐t②❀ ♦t❤❡rs ✕ ✈❡r② •♦✇ q✉❛•✐t②✱ ❡t❝✳ ❇② ❝❤♦♦s✐♥❣ ❛ s❡t ♦❢ r❡✈✐❡✇❡rs✱ t❤❡ ✜r♠ ❝❛♥ ❝❤♦♦s❡ ✇❤✐❝❤ st❛t❡s ❛r❡ r❡✈❡❛•❡❞✳ ❆s ❛♥♦t❤❡r ❡①❛♠♣•❡✱ ❝♦♥s✐❞❡r ❛♥ ❛✉t❤♦r✐t❛r✐❛♥ ❣♦✈❡r♥♠❡♥t t❤❛t s❡❡❦s t♦ ♠❛①✐♠✐s❡ t❤❡ ♥✉♠❜❡r ♦❢ ❝✐t✐③❡♥s t❤❛t t❛❦❡ ❛ ❝❡rt❛✐♥ ❛❝t✐♦♥ ✭s✉❝❤ ❛s ✈♦t✲ ✐♥❣ ❢♦r t❤❡ ❣♦✈❡r♥♠❡♥t✱ •♦✐♥✐♥❣ ❛ ♣r♦✲❣♦✈❡r♥♠❡♥t r❛••②✱ ♦r r❡❢✉s✐♥❣ t♦ •♦✐♥ ❛♥ ❛♥t✐✲❣♦✈❡r♥♠❡♥t ♣r♦t❡st✮✳ ❆ ❝✐t✐③❡♥✬s ✇✐••✐♥❣♥❡ss t♦ ❞♦ s♦ ❞❡♣❡♥❞s ♦♥ ❤❡r t②♣❡ ✭✇❤✐❝❤ ♠❡❛s✉r❡s t❤❡ ❞❡❣r❡❡ t♦ ✇❤✐❝❤ s❤❡ s✉♣♣♦rts t❤❡ ❣♦✈❡r♥♠❡♥t✬s ✐❞❡♦•♦❣②✮✱ ❛♥❞ ♦♥ t❤❡ ♥❡✇s ✭✇❤✐❝❤ ✐s ❛ ♠❡❛s✉r❡ ♦❢ ❤♦✇ ❝♦♠♣❡t❡♥t t❤❡ ❣♦✈❡r♥✲ ♠❡♥t ✐s✮ ✶ ✳ ❚❤❡ ❣♦✈❡r♥♠❡♥t ❝❛♥ r❡str✐❝t t❤❡ s❡t ♦❢ ❛✈❛✐•❛❜•❡ ♥❡✇s ❜② ❝❤♦♦s✐♥❣ ✇❤✐❝❤ ✐♥❞❡♣❡♥❞❡♥t ♠❡❞✐❛ ♦✉t•❡ts ❛r❡ ❛••♦✇❡❞ t♦ ♦♣❡r❛t❡ ✐♥ t❤❡ ❝♦✉♥tr② ✷ ✳ ❚❤❡ ❦❡② ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤✐s ♣❛♣❡r ✐s ✐♥ ❞❡✈❡•♦♣✐♥❣ ❛ ♥♦✈❡• ❛♣♣r♦❛❝❤ t♦ ✜♥❞✐♥❣ t❤❡ ♦♣t✐♠❛• ❝❡♥s♦rs❤✐♣ s❝❤❡♠❡ ✇❤❡♥ t❤❡ s❡♥❞❡r ✐s ❝♦♥str❛✐♥❡❞ t♦ ❝❡♥s♦rs❤✐♣ str❛t❡❣✐❡s✳ ❙♣❡❝✐✜❝❛••②✱ t❤❡ ♣❛♣❡r t❛❦❡s ❛ ❞✐r❡❝t ♦♣t✐♠✐s❛t✐♦♥ ❛♣✲ ♣r♦❛❝❤✿ ❢♦r ❛ ❣✐✈❡♥ ❝❡♥s♦rs❤✐♣ str❛t❡❣② ✐t ❝❤❡❝❦s ✇❤❡t❤❡r ♣r♦✜t❛❜•❡ ❞❡✈✐❛t✐♦♥s ✶ ❚❤✉s✱ t❤❡ ❝✐t✐③❡♥ ✇❛♥ts t♦ s✉♣♣♦rt t❤❡ ❣♦✈❡r♥♠❡♥t ✇❤❡♥ ❤✐s ❜❡•✐❡❢ ✐♥ t❤❡ ❣♦✈❡r♥♠❡♥t✬s ❝♦♠♣❡t❡♥❝❡ ♦✉t✇❡✐❣❤s ❤✐s ❞✐s•✐❦❡ ♦❢ t❤❡ ❣♦✈❡r♥♠❡♥t✬s ✐❞❡♦•♦❣②✳ ❚❤✐s ✐s ✐♥ •✐♥❡ ✇✐t❤ ♠♦❞❡•s ♦❢ ❡①♣r❡ss✐✈❡ ✈♦t✐♥❣ ✭❇r❡♥♥❛♥ ❛♥❞ ❍❛♠•✐♥✱ ✶✾✾✽✮✱ ✐♥ ✇❤✐❝...

A biased newspaper aims to persuade voters to vote for the government. Voters are uncertain about the government’s competence. Each voter receives the newspaper’s report as well as independent private signals about the competence. Voters then exchange messages containing this information on social media and form posterior beliefs, neglecting correlation among messages. We show that greater social connectivity increases the probability of an efficient voting outcome if the prior favours the government; otherwise, efficiency decreases. The probability of an efficient outcome remains strictly below one even when connectivity becomes large, implying a failure of the Condorcet jury theorem.

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We propose a model of political persuasion in which a biased newspaper aims to convince voters to vote for the government. Each voter receives the newspaper's report, as well as an independent private signal. Voters then exchange this information on social media and form posterior beliefs, neglecting correlation among signals. An increase in connectivity increases the newspaper's bias if voters are ex ante predisposed to vote against the government, and reduces the bias if they are predisposed in favour of the government. While more precise independent signals reduce the newspaper's optimal bias, the bias remains positive even when connectivity becomes large. Thus, even with a large number of social connections, the election produces an inefficient outcome with positive probability, implying a failure of the Condorcet jury theorem.