If an effect says "You may search your library . . . If you do, shuffle your library," and you haven't paid , you can't choose to search, so you won't shuffle.

If an effect says "Search your library . . . Then shuffle your library," and you haven't paid , the search effect fails, but you will still have to shuffle.

Since players who haven't paid can't search, they won't be able to find any cards in a library. The effect applies to all players and all libraries. If a spell or ability's effect has other parts that don't depend on searching for or finding cards, they will still work normally.

Effects that tell a player to reveal cards from a library or look at cards from the top of a library will still work. Only effects that use the word "search" will fail unless a player pays .

Paying to ignore Leonin Arbiter's effect is a special action. Any player may take this special action any time he or she has priority. It doesn't use the stack and can't be responded to.

Paying doesn't let a player pick up a library and search it -- it just allows him or her to ignore Leonin Arbiter's effect that turn. That player can search a library only if another spell or ability instructs him or her to do so.

If a player pays , that enables only him or her to ignore Leonin Arbiter's effect that turn. Each other player is still affected by it.

A player who has paid may search any library when instructed to do so that turn, not just his or her own library.

Once a player has paid , he or she may search libraries that turn as many times as he or she is instructed to do so.

If there are multiple Leonin Arbiters on the battlefield, a player must pay for each one before being able to search libraries that turn.