Electoral disputes arising out of Presidential and Vice-Presidential Elections are settled by the Supreme Court of India.

Option 1, the Election Commission of India, is responsible for conducting and overseeing elections in the country but does not have the authority to settle electoral disputes for these specific elections.

Option 2, the Joint Committee of Parliament, does not have jurisdiction over electoral disputes. It is a committee formed by members of both houses of Parliament to discuss and deliberate on specific issues.

Option 4, the Speaker of Lok Sabha, is responsible for the management and functioning of the Lok Sabha (the lower house of Parliament) and does not have the authority to resolve electoral disputes.

The correct answer is option 3 because the Supreme Court of India has the final authority to resolve electoral disputes arising from Presidential and Vice-Presidential Elections. The Supreme Court is the highest judicial body in the country and has the power of judicial review, making it the appropriate institution to settle such disputes.