n. [ Pref. a- not + methodist. ] One without method; a quack. [ Obs. ] [ 1913 Webster ]

. (Physics) A method of attaining successively lower temperatures by utilizing the cooling effect of the expansion of one gas in condensing another less easily liquefiable, and so on. [ Webster 1913 Suppl. ]

Condorcet's method is one of several pairwise methods, which are great methods for electing people in single-seat elections (president, governor, mayor, etc.). Condorcet's method is named after the 18th century election theorist who invented it. Unlike most methods which make you choose the lesser of two evils, Condorcet's method and other pairwise methods let you rank the candidates in the order in which you would see them elected. The way the votes are tallied is by computing the results of separate pairwise elections between all of the candidates, and the winner is the one that wins a majority in all of the pairwise elections.
The best result of this is that if there is Candidate A on one extreme who pulls 40% of the vote, Candidate B in the middle who only pulls 20% of the vote, and Candidate C on the other extreme who pulls 40% of the vote, Candidate B will get elected as a compromise. Why? Because in a two-way contest between A and B, B would win with 60% of the vote, and in a two-way contest between B and C, B would also win with 60% of the vote. (Note that if B is a loony billionaire, he might not be able to win separate pairwise elections against anyone, and this would be reflected with Condorcet's method.)
Condorcet's method lets voters mark their sincere wishes for who they would like to win the election, without having to consider strategy ("I'd vote for Candidate B, but I'm afraid of wasting my vote."). It's really just a logical extension of majority rule when more than two choices are involved. Other pairwise methods, such as Copeland's method and Smith's method, have other desirable characteristics. The best of the pairwise methods is something that is quite debatable.
Wait, I've heard of this before...
You may have. However, there are many methods other methods similar to this one (though in my opinion, inferior), so don't be so sure. In order to be fair, here are a couple of those other methods:
* Majority preference voting (MPV) -- related to PV. Like PV, the voter simply ranks candidates in an order of preference (e. 1. Perot 2. Clinton 3. Bush). The candidate with the least number of first place votes is eliminated, and their votes are "transferred" to their 2nd choice until a candidate has a majority. It is frequently advocated and is better than our current system, but still has some nasty properties (like possibly knocking compromise candidates out of the running early). MPV is actually in use in Australia, among other places. Also known as Hare's Method.
* Approval -- Voters are allowed to vote for all candidates they approve. For example, Bush-Yes Perot-No Clinton-Yes. The candidate with the highest number of "yes" votes wins. For a more complete explanation, see here.
Rob Lanphier (from https://web.archive.org/web/20050722235546/http://www.eskimo.com/~robla/politics/condorcet.html). [ PJC ]

a. Not methodical; without method or systematic arrangement; without order or regularity; confused. Addison.

Syn. -- Irregular; confused; disoderly; unsystematic; desultory. [ 1913 Webster ]

adv. Without method; confusedly; unsystematically. [ 1913 Webster ]

n. Lack of method. [ 1913 Webster ]

v. t. To render immethodical; to destroy the method of; to confuse. [ R. ] [ 1913 Webster ]

n. A method of teaching by question and answer; it was used by Socrates to elicit truths from his students; -- called also the Socratic method [ WordNet 1.5 ]

n. [ F. méthode, L. methodus, fr. Gr. meqodos method, investigation following after; meta` after + "odo`s way.] 1. An orderly procedure or process; regular manner of doing anything; hence, manner; way; mode; as, a method of teaching languages; a method of improving the mind. Addison. [1913 Webster]

2. Orderly arrangement, elucidation, development, or classification; clear and lucid exhibition; systematic arrangement peculiar to an individual. [1913 Webster]

Though this be madness, yet there's method in it. Shak. [1913 Webster]

All method is a rational progress, a progress toward an end. Sir W. Hamilton. [1913 Webster]

3. (Nat. Hist.) Classification; a mode or system of classifying natural objects according to certain common characteristics; as, the method of Theophrastus; the method of Ray; the Linnaean method. [1913 Webster]

4. A technique used in acting in which the actor tries to identify with the individual personality of the specific character being portrayed, so as to provide a realistic rendering of the character's role. Also called the Method, method acting, the Stanislavsky Method or Stanislavsky System. [PJC]

Syn. -- Order; system; rule; regularity; way; manner; mode; course; process; means. -- Method, Mode, Manner. Method implies arrangement; mode, mere action or existence. Method is a way of reaching a given end by a series of acts which tend to secure it; mode relates to a single action, or to the form which a series of acts, viewed as a whole, exhibits. Manner is literally the handling of a thing, and has a wider sense, embracing both method and mode. An instructor may adopt a good method of teaching to write; the scholar may acquire a bad mode of holding his pen; the manner in which he is corrected will greatly affect his success or failure. [1913 Webster]

{ } a. [ L. methodicus, Gr. &unr_;: cf. F. méthodique. ] 1. Arranged with regard to method; disposed in a suitable manner, or in a manner to illustrate a subject, or to facilitate practical observation; well-ordered; as, the methodical arrangement of arguments; a methodical treatise. [ wns=2 ] “Methodical regularity.” Addison. [ 1913 Webster ]

2. Proceeding with regard to method; characterized by method or orderliness; systematic; as, a methodical investigation. [ wns=1 ] “Aristotle, strict, methodic, and orderly.” Harris. [ 1913 Webster ]

3. Of or pertaining to the ancient school of physicians called methodists. Johnson. [ 1913 Webster ]

-- Me*thod"ic*al*ly, adv. -- Me*thod"ic*al*ness, n. [ 1913 Webster ]

n. The art and principles of method. [ 1913 Webster ]

n. (Eccl.) The system of doctrines, polity, and worship, of the sect called Methodists. Bp. Warburton. [ 1913 Webster ]

n. [ Cf. F. méthodiste. See Method. ] 1. One who observes method. [ Obs. ] [ 1913 Webster ]

2. One of an ancient school of physicians who rejected observation and founded their practice on reasoning and theory. Sir W. Hamilton. [ 1913 Webster ]

3. (Theol.) One of a sect of Christians, the outgrowth of a small association called the “Holy Club, ” formed at Oxford University, a. d. 1729, of which the most conspicuous members were John Wesley and his brother Charles Wesley; -- originally so called from the methodical strictness of members of the club in all religious duties. [ 1913 Webster ]

4. A person of strict piety; one who lives in the exact observance of religious duties; -- sometimes so called in contempt or ridicule. [ 1913 Webster ]

a. Of or pertaining to the sect of Methodists; as, Methodist hymns; a Methodist elder. [ 1913 Webster ]

{ } a. Of or pertaining to methodists, or to the Methodists. -- Meth`o*dis"tic*al*ly, adv. [1913 Webster]

n. The act or process of methodizing, or the state of being methodized. [ 1913 Webster ]

v. t. [ imp. & p. p. Methodized p. pr. & vb. n. Methodizing ] To reduce to method; to dispose in due order; to arrange in a convenient manner; as, to methodize one's work or thoughts. Spectator. [ 1913 Webster ]

n. One who methodizes. [ 1913 Webster ]

a. Of or pertaining to methodology. [ 1913 Webster ]

n. [ Gr. &unr_; method + -logy. ] The science of method or arrangement; a treatise on method. Coleridge. [ 1913 Webster ]

(Pedagogy) A system of training and instruction, primarily for use with normal children aged from three to six years, devised by Dr. Maria Montessori while teaching in the “Houses of Childhood” (schools in the poorest tenement districts of Rome, Italy), and first fully described by her in 1909. The fundamental aim is to create self-motivation for education, and the leading features are freedom for physical activity (no stationary desks and chairs), informal and individual instruction, the very early development of reading and writing skills, and an extended sensory and motor training (with special emphasis on vision, touch, perception of movement, and their interconnections), mediated by a patented, standardized system of “didactic apparatus, ” which is declared to be “auto-regulative.” Most of the chief features of the method are borrowed from current methods used in many institutions for training feeble-minded children, and dating back especially to the work of the French-American physician Edouard O. Seguin (1812-80). [ Webster 1913 Suppl. ]

. (Education) A method of teaching reading by giving first attention to phrases and sentences and later analyzing these into their verbal and alphabetic components; -- contrasted with alphabet method and word method. See also phonics. [ Webster 1913 Suppl. ]

. (Education) A method of teaching reading in which words are first taken as single ideograms and later analyzed into their phonetic and alphabetic elements; -- contrasted with alphabet method and sentence method. [ Webster 1913 Suppl. ]