What change has been the most impactful on the world of election administration?

Answer 1

The answer here depends on the time period you're looking at. For more recent developments, Christopher's answer fits very well, but if you're talking about the entire history of elections, then you'll have to go back a bit further.

Originally, even in areas with relatively widespread democratic institutions outside of ancient Athens, the "electorate" consisted only of landowners; not only women, but also poorer men, including merchants and unlanded sons, were excluded from the political process. Early in American history, however, people began interpreting "all men are created equal" to not be in opposition to landed European-style "divine right" aristocracies, but rather in support of the notion that all men (well, at the time, white men) deserved a say in the political sphere.

Following this expansion of suffrage to those who don't own land, in the United States at least, the opening of suffrage to black men following the Civil War (even if in practice their votes were suppressed) and to women with the 19th amendment represent the biggest historical impacts to elections.

Answer 2

Elections are often considered amongst the most foundational elements of any democratic political system, and expanding the franchise to include every adult member of a polity is a critical policy endeavor to pursue. One way that this has increasingly been done in recent year is through absentee voting. While this has long existed amongst expats and members of the armed services, deliberately expanding to it include those within various municipalities has also positively impacted voter participation rates.

Especially in the United States, where voting is not mandated, and the conduct of elections is up to the whims of each individual state, there are often a multitude of barriers that preclude large swaths of the populations from voting with ease. Indeed, for many working-class Americans, even the fact that there is no federal election holiday (as similarly exists in many other developed democracies) proves to be a formidable obstacle. Allowing any registered voter to vote by mail in the weeks or even months ahead of a local, state and national election has proven to be a most impactful policy approach in this arena.