Induce, persuade, prevail, get are comparable when meaning to move another by arguments, entreaties, or promises to do or agree to something or to follow a recommended course.
Induce usually implies overcoming indifference, hesitation, or opposition especially by offering for consideration persuasive advantages or gains that depend upon the desired decision being made; the term usually suggests that the decision is outwardly at least made by the one induced rather than forced upon him by the one that induces.
Persuade implies a winning over by an appeal, entreaty, or expostulation addressed as much to feelings as to reason; it usually implies that the one persuaded is more or less won over by the one that persuades.
Prevail, usually with on or upon , may be employed in place of either induce or persuade , but it usually carries a stronger implication of opposition to be faced or of good arguments to be overcome.
Get in this relation (see also GET 1 ) is a much more neutral term than the others discriminated and it may replace any of them when the method by which a favorable decision is brought about is irrelevant or, sometimes, is deliberately not stressed.