This was known long before the time of Hort, and those proposing minority readings were conscious of having to counter the a priori weight of the majority of manuscripts.
"Had we reason to believe that all these authorities were of equal value, our course would be a simple one....we should simply reckon up the number upon opposing sides, and pronounce our verdict according to the numerical majority. ...however, ... in a court of justice ... evidence given by different witnesses differs [greatly]. ... to merely [count] our witnesses will not do. We must distinguish their individual values. ...Were we to be guided by the number of witnesses [only] on either side, we would at once have to favour of the Received Text."
- W. Milligan ( The Words of the NT, 1873)
While insisting on the need for weighing witnesses, Milligan here openly concedes what everyone knows: Most readings in the Textus Receptus (TR) are supported by an overwhelming majority of manuscripts.
Milligan's own proposals avoid any direct attempt to debate the value of landslide majority readings. Instead, he uses a crude procedure of dividing MSS into 'early' and 'late': His fundamental axiom is that older manuscripts and their readings are better. From this universal assumption, all 'early' MSS and their readings are simply given a priori preference over their numerically vastly superior, but mostly later rivals. Assigning priority by fiat, he avoids having to deal with probability arguments regarding MS counts.
This arbitrary method however does nothing to actually refute the reasonable presumption that, all other things being equal, the majority reading is most probably original.
Hort himself knew the fallacy of Milligan's simplistic solution, for he insists,
"But the occasional preservation of comparatively ancient texts in comparatively modern MSS forbids confident reliance on priority of [MS] date unsustained by other marks of excellence." (Intro. p. 31)
Hort further conceded that for singular readings, the majority reading certainly did hold the probability of being correct:
"Where a minority consists of one document or hardly more, there is a valid presumption against the reading thus attested, because any one scribe is liable to err, whereas the fortuitous concurrence of a plurality of scribes in the same error is in most cases improbable;" (Ibid. p. 44)
Hort was certainly aware of the problem and power of a majority reading, and rather than dismiss it completely, he sought to severely limit its value. He spends many pages presenting hypothetical arguments in an attempt to minimize and/or eliminate the validity of majority readings (e.g Intro., pp.40-46). In order to override the weight of majority testimony, Hort in the main invokes the concept of genealogy. His methods and arguments have been critiqued elsewhere, so we won't go into them here.
But the argument based on the majority of MSS actually is itself essentially a genealogical argument, something for the most part ignored in the literature.
Here we will be free to explore both its strengths and weaknesses.