Learn Russian: Ведь избиратели считают этого кандидата достойным человеком. - After all, the voters consider this candidate a worthy person.

The verb считать (to consider) triggers this. When expressing that someone considers X to be Y, Russian uses the structure считать + [Accusative object] + [Instrumental role/quality]. Here, the voters consider the candidate (Accusative: этого кандидата) to be a worthy person (Instrumental: достойным человеком).

Why is the direct object этого кандидата instead of этот кандидат?

The verb считать takes a direct object in the accusative case. Because кандидат is an animate masculine noun (a living person), its accusative form changes to match the genitive case, resulting in этого кандидата.

What exact flavor does the word ведь add to the beginning of this sentence?

Ведь is a very common emphatic particle used to justify a statement or remind the listener of a shared fact. Translated here as 'after all,' it implies that the speaker is using the voters' opinion as proof or an argument for something said previously.

Does the verb считать always mean to consider?

Not always. Its primary literal meaning is 'to count' (like counting numbers, votes, or money). However, whenever you see it used with the Accusative + Instrumental pattern as it is in this sentence, it reliably shifts to the abstract meaning of 'to consider' or 'to deem.'