Concerning the persons who are properly entitled to vote in such an election, there has been some diversity of opinion. That all the male members of the church in what is called “full communion” have this right, there can be no question. In this, all are agreed. But, it has been maintained, not indeed with the same unanimity, yet it is believed by a large majority of the most judicious and enlightened judges, and probably on the most correct principles, that all baptized members of the church, who must be, of course, regarded as subject to the government and discipline administered by these rulers, are entitled to a voice in their election. And, where there are female heads of families who bear the relation of membership to the church in either of the senses just mentioned, and who are not represented by some qualified male relative on the occasion, it has been judged proper to allow them to vote in the choice of ruling elders, as is generally the case in the choice of a pastor.
From: An Essay on the Warrant, Nature, and Duties of the Office of the Ruling Elder in the Presbyterian Church, Together with a Sermon on the Ruling Elder Preached in Philadelphia, May 22, 1843 by Samuel Miller; reprint (Dallas: Presbyterian Heritage Publications, 1999), pp. 266-267. First published (minus the sermon) in 1831. The sermon was first published in 1844.
Samuel Miller (1769-1850) was Professor of Ecclesiastical History and Church Government at Princeton Theological Seminary in Princeton, New Jersey, from 1813 to 1848.