"government formed by election by ballot," by 1966, from Greek psēphizein "to vote" (properly "to vote with pebbles"), from psēphos "pebble, small stone," especially as used for counting and calculating (a word of uncertain origin, perhaps related to psammos "sand"), + -cracy "rule or government by."
The common method of voting in Greek cities was by dropping pebbles in different marked urns, and thus the word for "pebble" figures largely in the ancient Greek vocabulary of democracy (e.g. isopsēphos "having an equal vote"). Also a psēphados was "a juggler." Related: Psephocrat; psephocratic.
word-forming element meaning "a speaking, discourse, treatise, doctrine, theory, science," from Greek -logia (often via French -logie or Medieval Latin -logia), from -log-, combining form of legein "to speak, tell;" thus, "the character or deportment of one who speaks or treats of (a certain subject);" from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak (to 'pick out words')." Often via Medieval Latin -logia, French -logie. In philology "love of learning; love of words or discourse," apology, doxology, analogy, trilogy, etc., Greek logos "word, speech, statement, discourse" is directly concerned.
<a href="https://www.etymonline.com/word/psephology">Etymology of psephology by etymonline</a>
Harper, D. (n.d.). Etymology of psephology. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/psephology