Most political leaders acquire their position by causing a large number of people to believe that these leaders are ___________ by altruistic desires.

Some politicians nowadays make fake promises in trying to make people to vote for them, so they try tactics of deceiving voters to vote for them. They make others believe that they have altruistic (showing that you are unselfish and your actions are totally concentrated on helping others) motives.
Option (a) is correct, because it means motivated. The politicians make the voters believe that they are motivated by altruistic desires. Option (b) is wrong because convinced means that you are just in agreement with something. Option (c) is wrong, because categorized means to place in categories. Option (d) means that they are guided by altruistic desires, but the word motivate is more appropriate, as it shows a higher degree of effect.