Voting tests would let mature people vote. Maturity is the ability to use wisdom to make a good decision. If voters were mature, they'd vote for better political candidates and leaders. Having better political leaders would improve the country and government. Voters need to have sufficient knowledge and intelligence to make the correct choices at the ballot that will lead to prosperity. Many people vote without truly knowing what they're voting for, and people with prejudiced opinions or opinions that will bring about destruction can vote as well. The very reason the United States was designed as a republic instead of direct democracy is that the founding fathers knew that highly qualified, knowledgeable people (such as the electoral college and the senate) should be making the important decisions for a country, not random citizens.  A test to vote would ensure that citizens who want to participate in electing public and government officials have the maturity to lead the country in a positive direction.
Maturity is subjective. Someone’s idea of maturity is different than another. The designers of the test will be inherently biased and design the test to what they believe is maturity. Their idea of maturity will only be one conceptualization of maturity; no single test can accurately identify every single person that is mature enough to make good decisions. Requiring a maturity test in order to vote infringes upon a persons' right to elect officials into office. In addition, even "mature" people do not all hold the same beliefs, so only mature people voting would not prevent conflicts arising from varying political opinions.
Only mature people should be eligible to vote.
[P1] Mature voters will pass voting tests. [P2] Mature voters can vote for a better government than non-mature voters can.
Rejecting the premises
[Rejecting P1] Not everyone who passes the test will be a mature voter. You can’t test maturity because maturity is subjective. [Rejecting P2] Although making wise decisions will benefit the government, people are flawed and selfish. Even if the right politician was voted for, they are imperfect and prone to making mistakes.