An effect of the third party candidates such as theodore roosevelt on presidential elections is

They sometimes gain enough votes to cause a major party to lose

(Reasoning that might help you) there are usually only two major parties that have the most power in united states politics, even tho those parties have changed over time. Third party candidates, how ever are still able to influence elections . A third party can gain votes from people who would have other wise voted for one of the major parties, and enough of this votes can cause major party to lose. One of the most famous times this occured was in the 1912 presidential election, when theeodore roosevelt bull moose party signed voters who would have supported the republican william taft. The republican votes was split between roosevelt taft , so the democrat woodrow wison won the election.