Apex example of determining if two multi-select picklist fields contain similar values as asked by https://twitter.com/jeffereyberger/status/877214452453658628

DetermineCommonPicklistValues.java

// in apex, the values from multi-select
// picklists are simply delimited strings
String picklistA = 'Apple;Orange;Banana';		// obj1.picklist__c
String picklistB = 'Apple;Pear;Plum;Orange';	// obj2.picklist__c

// split the strings into individual values and store as unique sets
Set<String> picklistValuesA = new Set<String>( picklistA.split(';') );
Set<String> picklistValuesB = new Set<String>( picklistB.split(';') );

System.debug( 'picklistValuesA: ' + picklistValuesA );
System.debug( 'picklistValuesB: ' + picklistValuesB );

// determine which values belong in both sets
Set<String> commonValues = new Set<String>( picklistValuesA );
commonValues.retainAll( picklistValuesB );
System.debug( 'picklists have these common values: ' + commonValues ); // 'Apple', 'Orange'

// if the resulting set has any values in it then
// yes, the two picklists have that many similar values
Boolean haveAtLeastOneCommonValue = ( commonValues.size() > 0 );
System.debug( 'picklists have at least one common value? ' + haveAtLeastOneCommonValue );