Etymonline has this to say:
-ics
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).
So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.
Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:
-ic
suffix forming adjectives
- of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
[...]
[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]
[...]
-ics
suffix forming nouns (functioning as singular)
- indicating a science, art, or matters relating to a particular subject: aeronautics, politics
- indicating certain activities or practices: acrobatics
[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]
The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".
The first sentence features ellipsis, that is, the omission of elements which are recoverable from the linguistic context or the situation. A full version would be on both the sender side and the receiver side. Once we reach the end of the sentence we can recover side and place it in our minds after sender. That’s not too difficult to do because the missing element occurs within a few words. However, some readers might be uncomfortable in performing that little bit of linguistic gymnastics, and that is presumably what the reviewer felt.
The answer to your question is that both sentences are grammatical, and both convey the same meaning. If you think your readers might have difficulty with the omission of side after sender, then use the version that uses the plural: on both the sender and the receiver sides. Alternatively, use the full version of the ellipted form with the singular: on both the sender side and the receiver side.
Best Answer
I think this usage is most likely to have developed from the other collective or general senses of "vote", which appear to have existed from the start of the word's use, rather than from a modification of the individualized sense "one person's vote" (the sense found in most plural uses of "votes").
It doesn't seem to be particularly recent in origin: I was able to find this example from 1915:
("The Nation-Wide Movement for Municipal Efficiency Under Direct Popular Control", Equity, Volumes 17-18, edited by Charles Fremont Taylor, page 186)
The Oxford English Dictionary (OED) defines the word vote using the word "opinion", and it might be helpful to note that we likewise can speak of one person's opinion, people's opinions, or of common opinion shared by multiple people.
The OED's definition 3a of "vote" is
with examples such as
[...]
It's possible that some examples are simply typos or abbreviations of another wording, although it seems difficult to explain away the entirety of your examples in this way. Like some of the commenters beneath your question, I would find it more natural to say "Percentage of the total vote cast by...", which would be expressed in headlinese as "percentage of total vote cast by". The example in Binstock 2000 is not headlinese, but I find it interesting that the rest of the document seems to generally use "of votes" in similar contexts; I almost wonder whether we can rule out "Percentage of total vote" in this source being a typo for "Percentage of total votes".