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Wikipedia has this:

###Joint or separate possession For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe

(e.g. "his and her children").

The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable

(e.g. ??"you and your spouse's bank account").

[??/*"Tim and your bank account"]).

The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)

Wikipedia has this:

Joint or separate possession

For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe

(e.g. "his and her children").

The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable

(e.g. ??"you and your spouse's bank account").

[??/*"Tim and your bank account"]).

The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)

Wikipedia has this:

###Joint or separate possession For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe

(e.g. "his and her children").

The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable

(e.g. ??"you and your spouse's bank account").

The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)

Wikipedia has this:

###Joint or separate possession For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe

(e.g. "his and her children").

The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable

(e.g. ??"you and your spouse's bank account").

[??/*"Tim and your bank account"]).

The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)

Wikipedia has this:

###Joint or separate possession For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe (e.g. "his and her children"). The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable ("you and your spouse's bank account"). The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)

Wikipedia has this:

###Joint or separate possession For two nouns (or noun phrases) joined by and, there are several ways of expressing possession, including:

1. marking of the last noun (e.g. "Jack and Jill's children")
2. marking of both nouns (e.g. "Jack's and Jill's children").

Some grammars make no distinction in meaning between the two forms. Some publishers' style guides, however, make a distinction, assigning the "segregatory" (or "distributive") meaning to the form "John's and Mary's" and the "combinatorial" (or "joint") meaning to the form "John and Mary's". A third alternative is a construction of the form "Jack's children and Jill's", which is always distributive, i.e. it designates the combined set of Jack's children and Jill's children.

When a coordinate possessive construction has two personal pronouns, the normal possessive inflection is used, and there is no apostrophe

(e.g. "his and her children").

The issue of the use of the apostrophe arises when the coordinate construction includes a noun (phrase) and a pronoun. In this case, the inflection of only the last item may sometimes be, at least marginally, acceptable

(e.g. ??"you and your spouse's bank account").

The inflection of both is normally preferred (e.g. Jack's and your dogs), but there is a tendency to avoid this construction, too, in favour of a construction that does not use a coordinate possessive (e.g. by using "Jack's letters and yours"). Where a construction like "Jack's and your dogs" is used, the interpretation is usually "segregatory" (i.e. not joint possession).

("General principles for the possessive apostrophe", in "Apostrophe")

So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)