R.I. Gen. Laws § 17-15-29: Number of votes required to nominate or elect.

In determining the nomination or election of a candidate at a primary election, the person receiving the largest number of votes, although less than a majority of all the votes cast for the candidates for a particular office, shall be declared nominated or elected. Where there is more than one person to be elected to a particular office or place, those persons equaling that number of officers to be elected to the office or place receiving the largest number of votes, although less than a majority of all the votes cast for all the candidates for the office or place, shall be declared nominated or elected, as the case may be, unless otherwise provided by existing law.