First off, you have a couple of bugs:

You can keep clicking the #alphabetical or #builtfilter buttons, and each time you do, it'll add the parameter. Even if it's already there. Yet the "reverse" buttons only replace/remove 1 instance. So if you have:

 /some/path?foo=bar

and click the alphabetical button again a couple of times, you get

 /some/path?foo=bar&sort=alphabetical&sort=alphabetical&sort=alphabetical

But you'll have to click #chronological an equal number of times, to "reset" everything, since only one &sort=alphabetical chunk is removed each time.

Secondly, I don't know the URL you're manipulating, but if there are no parameters to begin with, you end up with an invalid URL like:

/some/path&sort=alphabetical

Note that there's no ? to separate the query string from the path. Instead the & has ended up there - where it shouldn't be.

Also, if you URL has a fragment like #something, you'll be adding paramters after that, which won't work right. Like:

/some/path?foo=bar#fragment&sort=alphabetical

So first off, I'd recommend using jQuery's param method to create a well-formatted query string from an object:

var params = { sort: "", status: "built" }; // an example
var queryString = jQuery.param(params); //=> "sort=&status=built"

Secondly, you can use data-* attributes on your links to specify their action and classes to allow you to find all the links/buttons in one go (here's a related answer of mine).

For instance (simple example):

<button type="button" class="param" data-key="sort" data-value="alphabetical">Sort alphabetically</button>
<button type="button" class="param" data-key="sort" data-value="">Sort chronologically</button>

$(function () { // equivalent to $(document).ready(...)
  var params = { sort: "", status: "" }; // default params

  $(".param").on("click", function () {
    var $this = $(this),
        key = $this.data("param"),
        value = $this.data("value"),
        queryString;

    params[key] = value;
    queryString = jQuery.param(params);

    $(".subsection").attr("href", function () {
      // add or replace the query string as needed
      return this.href.replace(/(\?.*)?$/, "?" + queryString);
    });
  });
});

Note that this doesn't preserve fragments or any parameters that were already in the href, but not in the params object - but I'll leave that as an exercise.

First off, you have a couple of bugs:

You can keep clicking the #alphabetical or #builtfilter buttons, and each time you do, it'll add the parameter. Even if it's already there. Yet the "reverse" buttons only replace/remove 1 instance. So if you have:

 /some/path?foo=bar

and click the alphabetical button again a couple of times, you get

 /some/path?foo=bar&sort=alphabetical&sort=alphabetical&sort=alphabetical

But you'll have to click #chronological an equal number of times, to "reset" everything, since only one &sort=alphabetical chunk is removed each time.

Secondly, I don't know the URL you're manipulating, but if there are no parameters to begin with, you end up with an invalid URL like:

/some/path&sort=alphabetical

Note that there's no ? to separate the query string from the path. Instead the & has ended up there - where it shouldn't be.

Also, if you URL has a fragment like #something, you'll be adding paramters after that, which won't work right. Like:

/some/path?foo=bar#fragment&sort=alphabetical

So first off, I'd recommend using jQuery's param method to create a well-formatted query string from an object:

var params = { sort: "", status: "built" }; // an example
var queryString = jQuery.param(params); //=> "sort=&status=built"

Secondly, you can use data-* attributes on your links to specify their action and classes to allow you to find all the links/buttons in one go (here's a related answer of mine).

For instance (simple example):

<button type="button" class="param" data-key="sort" data-value="alphabetical">Sort alphabetically</button>
<button type="button" class="param" data-key="sort" data-value="">Sort chronologically</button>

$(function () { // equivalent to $(document).ready(...)
  var params = { sort: "", status: "" }; // default params

  $(".param").on("click", function () {
    var $this = $(this),
        key = $this.data("param"),
        value = $this.data("value"),
        queryString;

    params[key] = value;
    queryString = jQuery.param(params);

    $(".subsection").attr("href", function () {
      // add or replace the query string as needed
      return this.href.replace(/(\?.*)?$/, "?" + queryString);
    });
  });
});

Note that this doesn't preserve fragments or any parameters that were already in the href, but not in the params object - but I'll leave that as an exercise.