William R. Keech (later a professor of political science at UNC Chapel Hill) gave a presentation at the 1972 APSA (Amer. Polit. Sci. Assoc.) meeting arguing that the Republican 1964 presidential nominee "should" have been William Scranton, who was preferred pairwise over the actual nominee Barry Goldwater by a massive margin. I was unable to track this work down, but Keech & Matthews discussed the matter in their later book
William R. Keech & Donald R. Matthews: The Party's Choice, Brookings Institution, Washington DC 1977 with an epilogue concerning the 1976 nominations. (Also available electronically for money through the Questia online library.)
This book is a study of 10 presidential nomination decisions since 1936 (20 in all, since 2 parties). It, needless to say, has a low opinion of the parties' nomination processes, noting on page 114:
The record of the presidential primary system as it has operated in the opposition party since 1936 can thus be summed up as follows: When the party has a single front-runner, the primaries rarely change the situation. When the competitive situation within the party is more confused (1940, 1948, 1952, 1964), the primary system does little to facilitate the emergence of a single leader.
Anyhow, let's return to our main topic, the Republicans' disastrous decision to nominate Barry Goldwater in 1964, leading to, as Wikipedia called it, "one of the most lopsided presidential elections in United States history... Johnson crushed Goldwater in the general election, winning 61.1 percent of the popular vote, the largest percentage since the popular vote first became widespread in 1824 (up to the time of writing, 2006)" or as the New York Times 4 Nov. 1964 banner headline read, "JOHNSON SWAMPS GOLDWATER."
When your party loses to the largest popular vote ever recorded, it behooves you to ask: why? Well, according to Keech & Matthews p143-144:
As the Pennsylvania Governor [Scranton] frantically barnstormed the country, the Gallup polls showed that President Johnson was ahead of Goldwater by a 78 percent to 14 percent margin. The first choice preferences of Republican voters for their party's nominee were a stand-off between Goldwater (22 percent), Nixon (22 percent), Scranton (20 percent), and Lodge (21 percent), though if the race were narrowed to a two-way choice between Goldwater and Scranton, the Pennsylvania Governor came out comfortably ahead, 55 percent to 34 percent.
They also noted on page 142, concerning the primary in the largest state (California):
The chances for a Rockefeller victory in California seemed good. Polls taken after the Oregon primary [15 May] showed the first-choice preferences of the state's Republicans were almost evenly split between Rockefeller (26%), Lodge (24%), Goldwater (21%), and Nixon (21%). But given a forced choice between Rockefeller and Goldwater, [Rockefeller] came out well ahead... on June 2... Barry Goldwater won with 51.2% of the vote.
Different contest; same theme: plurality-system distortions caused by vote-splitting or strategic focusing by the voters on perceived "front runners" (at the time, nationally speaking, Goldwater was perceived to be one of the front runners despite his initial lack of popularity in California) caused somebody to win who it is known would have been beaten head-to-head by at least one opponent.
According to the second-hand report on Keech's 1972 presentation on page 531 of volume 9 issue 4 of Polity, year 1977 (unfortunately I never saw the primary source), Keech there went further, arguing that William Scranton was the Condorcet winner, and would have beat Goldwater pairwise by an even huger 60-to-34% margin.
Being the Condorcet winner is fine and dandy and means many a voting system would have nominated Scranton (e.g. see this for why range voting probably would have) – but not the system actually used, the plurality system, which nominated Goldwater to set the stage for the worst presidential defeat ever.