Final answer:
A presidential candidate might avoid campaigning in a state with a large number of electoral votes if it is a "safe" state, has a winner-take-all system that isn't competitive, or due to elector apathy. They focus their efforts where they can sway the outcome and gain electoral votes, often prioritizing swing states over states with a large but secure opposing majority.
Step-by-step explanation:
A presidential candidate might avoid campaigning in a state with a large number of electoral votes for several strategic reasons. One reason is the existence of "safe" states, where the outcome is virtually predetermined due to historical voting patterns. If a state is strongly leaning toward one party, the opposing candidate may perceive scarce opportunities to change that state's preference and therefore allocate resources to more competitive states, often called 'battleground' states. Such states can provide a better return on investment in terms of swaying the overall results of the Electoral College.
Another reason relates to the winner-take-all system in the Electoral College, used by forty-eight states and the District of Columbia. Candidates will focus their efforts on swing states where their campaigning can influence a close race, rather than in states where they are likely to lose or win by a large margin. Additionally, candidates need to be tactical about where they spend their time and resources during the election, as the goal is to win the Electoral College, not necessarily the popular vote. This was evident in instances such as the 2016 election, where candidates shifted their campaign focus to states that weren't traditionally contested but showed signs of changing voter behavior.
Furthermore, political apathy in the electorate also contributes to this strategy. If a candidate believes that the effort to mobilize their supporters will not be sufficient to overcome a significant lead by the opposition, it might be more strategic to concentrate on states where the electoral vote can be swayed by a smaller margin of the popular vote.