Wikipedia
During the game's development, Masaya Makamura, the president of Namco, was convinced that the Pac-Man ghosts should all be red, according to the Financial Times.
An intense internal battle ensued, led by then 26-year-old Namco developer Toru Iwatani, who was convinced that the game's villains should be multi-coloured.
In an interview with the Financial Times, Iwatani recounts the moment he confronted his boss:
Mr Nakamura was very scary. All the developers on the team, and all the people our age, knew that each ghost had to have a different colour?.?.?.?the ghosts needed to be cute like cartoons. But Mr Nakamura wanted them all red.
I was 26 years old, and it was terrifying to confront the boss. But I decided to hit him with data. I conducted an internal survey among my colleagues and, with my hands shaking, presented Mr Nakamura with the results. It was 40-0 in favour of coloured ghosts, and he agreed.
Making the ghosts "cute like cartoons" was a major part of the game's plan to entice women into arcades, Iwatani said. Iwatani's team considered several designs for the Pac-Man avatar, which could have been dominated by eyes or nose.
"The discussion didn't take very long," Iwatani said. "A few minutes. The character was all in the mouth."
It's safe to say that this design worked. Today, there is just one red ghost - Blinky. The others are pink, blue, and orange.