Rulings

• If an effect says "You may search your library . . . If you do, shuffle your library" or "You may search your library . . . then shuffle your library," you can't choose to search, so you won't shuffle.2011-01-01
• If an effect says "Search your library . . . then shuffle your library," you shuffle you libraries even though you can't search.2011-01-01
• Effects that instruct you to reveal or look at cards from the top of you library will still work. Only effects that use the word "search" are affected.2011-01-01
• Since players who haven't paid {2} 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.2011-01-01
• Paying {2} to ignore Leonin Arbiter's effect is a special action. Any player may take this special action any time they have priority. It doesn't use the stack and can't be responded to.2011-01-01
• Paying {2} doesn't let a player pick up a library and search it — it just allows them to ignore Leonin Arbiter's effect that turn. That player can search a library only if another spell or ability instructs them to do so.2011-01-01
• If a player pays {2}, that enables only them to ignore Leonin Arbiter's effect that turn. Each other player is still affected by it.2011-01-01
• A player who has paid {2} may search any library when instructed to do so that turn, not just their own library.2011-01-01
• Once a player has paid {2}, they may search libraries that turn as many times as they are instructed to do so.2011-01-01
• If there are multiple Leonin Arbiters on the battlefield, a player must pay {2} for each one before being able to search libraries that turn.2011-01-01