Repository: mui/material-ui (TypeScript)
Task: Bug Fix

Issue:
[Select] Aria error flagged by WAVE and W3C
<!-- Provide a general summary of the issue in the Title above -->
WAVE errors in tables, in TablePagination/TableFooter
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- [ x] The issue is present in the latest release.
- [x ] I have searched the [issues](https://github.com/mui-org/material-ui/issues) of this repository and believe that this is not a duplicate.

## Current Behavior 😯
1. Go to https://material-ui.com/components/tables/
2. Run WAVE
3. Should not get errors from standard components 
<!-- Describe what happens instead of the expected behavior. -->
WAVE identifies 3 "Broken ARIA Reference Errors" associated with three demos
- Sorting & Selection
- Fixed Headers
- Editable Example - this is a material-table which seems to inherit the accessibility bug from TableFooter 


## Expected Behavior 🤔
No WAVE errors
<!-- Describe what should happen. -->
No WAVE errors
## Steps to Reproduce 🕹
Given above
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Steps:

1.
2.
3.
4.

## Context 🔦

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## Your Environment 🌎
OSX Mojave, Chrome v80, WAVE v3.0.4
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  Include as many relevant details about the environment with which you experienced the bug.
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| Tech        | Version |
| ----------- | ------- |
| Material-UI | v4.9.6  |
| React       |         |
| Browser     |         |
| TypeScript  |         |
| etc.        |         |



Discussion:
Thanks for opening this issue.

Does WAVE provide more information beyond "Broken ARIA Reference Errors"?
## Broken ARIA reference

### What It Means

An aria-labelledby or aria-describedby reference exists, but the target for the reference does not exist.

### Why It Matters

ARIA labels and descriptions will not be presented if the element referenced does not exist in the page.

### How to Fix It
Ensure the element referenced in the aria-labelledby or aria-describedby attribute value is present within the page and presents a proper label or description.

### The Algorithm... in English

An element has an aria-labelledby or aria-describedby value that does not match the id attribute value of another element in the page.

### Standards and Guidelines

[1.3.1 Info and Relationships (Level A)](https://webaim.org/standards/wcag/checklist#sc1.3.1)
[4.1.2 Name, Role, Value (Level A)](https://webaim.org/standards/wcag/checklist#sc4.1.2)
@mfsjr Thanks for the report.

While this issue **focuses on the reported errors**. WAVE also reports less important alerts, I will take care of it in batch (e.g. broken anchor link).
@eps1lon If you would prefer working on it, I can leave it to you. Let me know, I wouldn't want to distract you from the prop-types -> TypeScript migration of the descriptions :D.
@oliviertassinari No perfectly fine. That's why I assigned it to you and unsubscribed. But you had to mention me again :stuck_out_tongue: 
Thank you @oliviertassinari , @eps1lon for such quick response!

Patch:
diff --git a/docs/src/pages/components/selects/MultipleSelect.js b/docs/src/pages/components/selects/MultipleSelect.js
--- a/docs/src/pages/components/selects/MultipleSelect.js
+++ b/docs/src/pages/components/selects/MultipleSelect.js
@@ -161,6 +161,7 @@ export default function MultipleSelect() {
             return selected.join(', ');
           }}
           MenuProps={MenuProps}
+          inputProps={{ 'aria-label': 'Without label' }}
         >
           <MenuItem disabled value="">
             <em>Placeholder</em>
diff --git a/docs/src/pages/components/selects/MultipleSelect.tsx b/docs/src/pages/components/selects/MultipleSelect.tsx
--- a/docs/src/pages/components/selects/MultipleSelect.tsx
+++ b/docs/src/pages/components/selects/MultipleSelect.tsx
@@ -163,6 +163,7 @@ export default function MultipleSelect() {
             return (selected as string[]).join(', ');
           }}
           MenuProps={MenuProps}
+          inputProps={{ 'aria-label': 'Without label' }}
         >
           <MenuItem disabled value="">
             <em>Placeholder</em>
diff --git a/docs/src/pages/components/selects/SimpleSelect.js b/docs/src/pages/components/selects/SimpleSelect.js
--- a/docs/src/pages/components/selects/SimpleSelect.js
+++ b/docs/src/pages/components/selects/SimpleSelect.js
@@ -57,7 +57,13 @@ export default function SimpleSelect() {
         <FormHelperText>Some important helper text</FormHelperText>
       </FormControl>
       <FormControl className={classes.formControl}>
-        <Select value={age} onChange={handleChange} displayEmpty className={classes.selectEmpty}>
+        <Select
+          value={age}
+          onChange={handleChange}
+          displayEmpty
+          className={classes.selectEmpty}
+          inputProps={{ 'aria-label': 'Without label' }}
+        >
           <MenuItem value="">
             <em>None</em>
           </MenuItem>
@@ -160,7 +166,13 @@ export default function SimpleSelect() {
         <FormHelperText>Auto width</FormHelperText>
       </FormControl>
       <FormControl className={classes.formControl}>
-        <Select value={age} onChange={handleChange} displayEmpty className={classes.selectEmpty}>
+        <Select
+          value={age}
+          onChange={handleChange}
+          displayEmpty
+          className={classes.selectEmpty}
+          inputProps={{ 'aria-label': 'Without label' }}
+        >
           <MenuItem value="" disabled>
             Placeholder
           </MenuItem>
diff --git a/docs/src/pages/components/selects/SimpleSelect.tsx b/docs/src/pages/components/selects/SimpleSelect.tsx
--- a/docs/src/pages/components/selects/SimpleSelect.tsx
+++ b/docs/src/pages/components/selects/SimpleSelect.tsx
@@ -59,7 +59,13 @@ export default function SimpleSelect() {
         <FormHelperText>Some important helper text</FormHelperText>
       </FormControl>
       <FormControl className={classes.formControl}>
-        <Select value={age} onChange={handleChange} displayEmpty className={classes.selectEmpty}>
+        <Select
+          value={age}
+          onChange={handleChange}
+          displayEmpty
+          className={classes.selectEmpty}
+          inputProps={{ 'aria-label': 'Without label' }}
+        >
           <MenuItem value="">
             <em>None</em>
           </MenuItem>
@@ -162,7 +168,13 @@ export default function SimpleSelect() {
         <FormHelperText>Auto width</FormHelperText>
       </FormControl>
       <FormControl className={classes.formControl}>
-        <Select value={age} onChange={handleChange} displayEmpty className={classes.selectEmpty}>
+        <Select
+          value={age}
+          onChange={handleChange}
+          displayEmpty
+          className={classes.selectEmpty}
+          inputProps={{ 'aria-label': 'Without label' }}
+        >
           <MenuItem value="" disabled>
             Placeholder
           </MenuItem>
diff --git a/packages/material-ui/src/Select/SelectInput.js b/packages/material-ui/src/Select/SelectInput.js
--- a/packages/material-ui/src/Select/SelectInput.js
+++ b/packages/material-ui/src/Select/SelectInput.js
@@ -26,6 +26,7 @@ function isEmpty(display) {
  */
 const SelectInput = React.forwardRef(function SelectInput(props, ref) {
   const {
+    'aria-label': ariaLabel,
     autoFocus,
     autoWidth,
     children,
@@ -320,8 +321,9 @@ const SelectInput = React.forwardRef(function SelectInput(props, ref) {
         tabIndex={tabIndex}
         role="button"
         aria-expanded={open ? 'true' : undefined}
-        aria-labelledby={`${labelId || ''} ${buttonId || ''}`}
         aria-haspopup="listbox"
+        aria-label={ariaLabel}
+        aria-labelledby={[labelId, buttonId].filter(Boolean).join(' ') || undefined}
         onKeyDown={handleKeyDown}
         onMouseDown={disabled || readOnly ? null : handleMouseDown}
         onBlur={handleBlur}
@@ -379,6 +381,10 @@ const SelectInput = React.forwardRef(function SelectInput(props, ref) {
 });
 
 SelectInput.propTypes = {
+  /**
+   * @ignore
+   */
+  'aria-label': PropTypes.string,
   /**
    * @ignore
    */
diff --git a/packages/material-ui/src/TablePagination/TablePagination.js b/packages/material-ui/src/TablePagination/TablePagination.js
--- a/packages/material-ui/src/TablePagination/TablePagination.js
+++ b/packages/material-ui/src/TablePagination/TablePagination.js
@@ -35,9 +35,9 @@ export const styles = (theme) => ({
   caption: {
     flexShrink: 0,
   },
+  // TODO v5: `.selectRoot` should be merged with `.input`
   /* Styles applied to the Select component root element. */
   selectRoot: {
-    // `.selectRoot` should be merged with `.input` in v5.
     marginRight: 32,
     marginLeft: 8,
   },
@@ -122,6 +122,7 @@ const TablePagination = React.forwardRef(function TablePagination(props, ref) {
             input={<InputBase className={clsx(classes.input, classes.selectRoot)} />}
             value={rowsPerPage}
             onChange={onChangeRowsPerPage}
+            inputProps={{ 'aria-label': labelRowsPerPage }}
             {...SelectProps}
           >
             {rowsPerPageOptions.map((rowsPerPageOption) => (


Test patch:
diff --git a/packages/material-ui/src/Select/Select.test.js b/packages/material-ui/src/Select/Select.test.js
--- a/packages/material-ui/src/Select/Select.test.js
+++ b/packages/material-ui/src/Select/Select.test.js
@@ -409,7 +409,7 @@ describe('<Select />', () => {
       const { getByRole } = render(<Select value="" />);
 
       // TODO what is the accessible name actually?
-      expect(getByRole('button')).to.have.attribute('aria-labelledby', ' ');
+      expect(getByRole('button')).to.not.have.attribute('aria-labelledby');
     });
 
     it('is labelled by itself when it has a name', () => {
@@ -417,7 +417,7 @@ describe('<Select />', () => {
 
       expect(getByRole('button')).to.have.attribute(
         'aria-labelledby',
-        ` ${getByRole('button').getAttribute('id')}`,
+        getByRole('button').getAttribute('id'),
       );
     });